Student: allan cranford Date: 9/13/16 Instructor: Basu Dipanker Course: MAT-240-Q6622-16EW6 Assignment: 5-2 MyStatLab: Module Five Problem Set 1. Determine whether the following sampling is dependent or independent. Indicate whether the response variable is qualitative or quantitative. A researcher wishes to compare annual salaries of mathematicians and non-mathematicians. She obtains a random sample of 132 professionals of each category who work and determines each individual's annual salary. Determine whether the following sampling is dependent or independent. A. The sampling is independent because an individual selected for one sample does dictate which individual is to be in the second sample. B. The sampling is independent because an individual selected for one sample does not dictate which individual is to be in the second sample. C. The sampling is dependent because an individual selected for one sample does dictate which individual is to be in the second sample. D. The sampling is dependent because an individual selected for one sample does not dictate which individual is to be in the second sample. Indicate whether the response variable is qualitative or quantitative. A. The variable is qualitative because it classifies the individual. B. The variable is qualitative because it is a numerical measure. C. The variable is quantitative because it is a numerical measure. D. The variable is quantitative because it classifies the individual. 2. An educator wants to determine whether a new curriculum significantly improves standardized test scores for students. She randomly divides 60 students into two groups. Group 1 is taught using the traditional curriculum, while group 2 is taught using the new curriculum. At the end of the school year, both groups are given the standardized test and the mean scores are compared. Determine whether the sampling is dependent or independent. Indicate whether the response variable is qualitative or quantitative. Determine whether the sampling is dependent or independent. A. This sampling is independent because the individuals selected for one sample do not dictate which individuals are to be in a second sample. B. The sampling is dependent because the individuals selected to be in one sample are used to determine the individuals to be in the second sample. C. The sampling is dependent because the individuals selected for one sample do not dictate which individuals are to be in a second sample. D. The sampling is independent because the individuals selected to be in one sample are used to determine the individuals to be in the second sample. Indicate whether the response variable is qualitative or quantitative. A. The variable is qualitative because it classifies the individual. B. The variable is qualitative because it is a numerical measure. C. The variable is quantitative because it is a numerical measure. D. The variable is quantitative because it classifies the individual. 3. Conduct a test at the = 0.10 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume the samples were obtained independently from a large population using simple random sampling. Test whether p1 > p2 . The sample data are x1 = 126, n1 = 249, x2 = 138, and n2 = 315. (a) Choose the correct null and alternative hypotheses below. A. H0 : p1 = 0 versus H1 : p1 0 B. H0 : p1 = p2 versus H1 : p1 > p2 C. H0 : p1 = p2 versus H1 : p1 p2 D. H0 : p1 = p2 versus H1 : p1 < p2 (b) Determine the test statistic. z0 = (Round to two decimal places as needed.) (c) Determine the P-value. The P-value is . (Round to three decimal places as needed.) What is the result of this hypothesis test? A. Reject the null hypothesis because there is sufficient evidence to conclude that p1 < p2 . B. Reject the null hypothesis because there is sufficient evidence to conclude that p1 > p2 . C. Do not reject the null hypothesis because there is not sufficient evidence to conclude that p1 < p2 . D. Do not reject the alternative hypothesis because there is sufficient evidence to conclude that p1 p2 . 4. Construct a confidence interval for p1 p2 at the given level of confidence. x1 = 351, n1 = 525, x2 = 413, n2 = 587, 99% confidence The 99% confidence interval for p1 p2 is ( , (Use ascending order. Round to three decimal places as needed.) ). 5. In a clinical trial of a vaccine, 12,000 children were randomly divided into two groups. The subjects in group 1 (the experimental group) were given the vaccine while the subjects in group 2 (the control group) were given a placebo. Of the 6,000 children in the experimental group, 84 developed the disease. Of the 6,000 children in the control group, 101 developed the disease. Determine whether the proportion of subjects in the experimental group who contracted the disease is less than the proportion of subjects in the control group who contracted the disease at the = 0.10 level of significance. Choose the correct null and alternative hypotheses below. A. H0 : p1 = p2 versus H1 : p1 p2 B. H0 : p1 = p2 versus H1 : p1 < p2 C. H0 : p1 = p2 versus H1 : p1 > p2 D. H0 : p1 = 0 versus H1 : p1 < 0 Determine the test statistic. z0 = (Round to two decimal places as needed.) Determine the P-value. The P-value is . (Round to three decimal places as needed.) What is the result of this hypothesis test? A. Reject the null hypothesis because there is not sufficient evidence to conclude that the proportion of subjects in the experimental group who contracted the disease is less than the proportion of subjects in the control group at = 0.10. B. Do not reject the null hypothesis because there is sufficient evidence to conclude that the proportion of subjects in the experimental group who contracted the disease is less than the proportion of subjects in the control group at = 0.10. C. Do not reject the null hypothesis because there is not sufficient evidence to conclude that the proportion of subjects in the experimental group who contracted the disease is less than the proportion of subjects in the control group at = 0.10. D. Reject the null hypothesis because there is sufficient evidence to conclude that the proportion of subjects in the experimental group who contracted the disease is less than the proportion of subjects in the control group at = 0.10. 6. Fill in the blank below. A researcher wants to show the mean from population 1 is less than the mean from population 2 in matched-pairs data. If the observations from sample 1 are Xi and the observations from sample 2 are Yi, and di = Xi Yi, then the null hypothesis is H0: d = 0 and the alternative hypothesis is H1: d ___ 0. A researcher wants to show the mean from population 1 is less than the mean from population 2 in matched-pairs data. If the observations from sample 1 are Xi and the observations from sample 2 are Yi, and di = Xi Yi, then the null hypothesis is H0: d = 0 and the alternative hypothesis is H1: d (1) (1) < 0. > 7. The following data represent the muzzle velocity (in feet per second) of shells fired from a 155-mm gun. For each shell, two measurements of the velocity were recorded using two different measuring devices, resulting in the following data. Observation A B 1 793.5 795.4 2 794.5 795.9 3 790.3 795.7 4 791.9 798.6 5 793.3 789.5 6 791.1 790.6 (a) Why are these matched-pairs data? A. The same round was fired in every trial. B. All the measurements came from rounds fired from the same gun. C. The measurements (A and B) are taken by the same instrument. D. Two measurements (A and B) are taken on the same round. (b) Is there a difference in the measurement of the muzzle velocity between device A and device B at the = 0.01 level of significance? Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. What is your conclusion regarding H0 ? Do not reject H0 . Reject H0 . (c) Construct a 99% confidence interval about the population mean difference. Compute the difference as device A minus device B. Interpret your results. The confidence interval is ( , (Round to three decimal places as needed.) ). Choose the statement that best agrees with your interpretion of your results. A. I am 13% confident that the mean difference in measurement is 0.01. B. I am 99% confident that the mean difference in measurement lies in the interval found above. C. I am 13% confident that the mean difference in measurement is 0. D. I am 1% confident that the mean difference in measurement lies in the interval found above. 8. A researcher studies water clarity at the same location in a lake on the same dates during the course of a year and repeats the measurements on the same dates 5 years later. The researcher immerses a weighted disk painted black and white and measures the depth (in inches) at which it is no longer visible. The collected data is given in the table below. Complete parts (a) and (b) below. Observation Date Initial After five years 1 1/25 72.5 79.3 2 3/19 52.3 53.1 3 5/30 38.4 38.0 4 7/3 47.9 48.1 5 9/13 68.2 75.9 6 11/7 35.9 43.3 (a) Why is it important to take the measurements on the same date? A. Using the same dates makes it easier to remember to take samples. B. Those are the same dates that all biologists use to take water clarity samples. C. Using the same dates makes the second sample dependent on the first. D. Using the same dates maximizes the difference in water clarity. (b) Does the evidence suggest that the clarity of the lake is improving at the = 0.05 level of significance? Note that the normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. Choose the correct conclusion below. Reject H0 . Do not reject H0 . 9. A researcher randomly selects 6 fathers who have adult sons and records the fathers' and sons' heights to obtain the data below. Determine if sons are taller than their fathers at the = 0.1 level of significance. The normal probability plot and boxplot indicate that the differences are approximately normally distributed with no outliers. Observation Height of father (in inches) Height of son (in inches) 1 2 3 4 5 6 68.1 72.9 65.8 72.4 66.8 67.9 69.2 76.7 64.2 77.2 70.5 68.3 Using the differences (father's height) (son's height), what is your conclusion regarding H0 ? Do not reject H0 because t0 is less than t . Do not reject H0 because t0 is greater than t . Reject H0 because t0 is greater than t . Reject H0 because t0 is less than t . 10. Assuming that both populations are normally distributed, construct a 95% confidence interval about 1 2 . (1 represents the mean of the experimental group and 2 represents the mean of the control group.) n x s The confidence interval has a lower bound of and an upper bound of (Use ascending order. Round to two decimal places as needed.) Experimental 20 47.3 7 . Control 25 40.7 10.9 11. Test whether 1 < 2 at the = 0.01 level of significance for the sample data shown in the accompanying table. Assume that the populations are normally distributed. 1 Click the icon to view the data table. Determine the null and alternative hypothesis for this test. A. H0 :1 = 2 H1 :1 2 B. H0 :1 < 2 H1 :1 = 2 C. H0 :1 2 H1 :1 < 2 D. H0 :1 = 2 H1 :1 < 2 Detemine the P-value for this hypothesis test. P= (Round to three decimal places as needed.) State the appropriate conclusion. Choose the correct answer below. A. Do not reject H0 . There is not sufficient evidence at the = 0.01 level of significance to conclude that 1 < 2 . B. Reject H0 . There is not sufficient evidence at the = 0.01 level of significance to conclude that 1 < 2 . C. Reject H0 . There is sufficient evidence at the = 0.01 level of significance to conclude that 1 < 2 . D. Do not reject H0 . There is sufficient evidence at the = 0.01 level of significance to conclude that 1 < 2 . 1: Sample Data n x s Population 1 Population 2 103.5 114.5 31 12.2 25 13.3 12. In baseball, league A allows a designated hitter (DH) to bat for the pitcher, who is typically a weak hitter. In league B, the pitcher must bat. The common belief is that this results in league A teams scoring more runs. In interleague play, when league A teams visit league B teams, the league A pitcher must bat. So, if the DH does result in more runs, it would be expected that league A teams will score fewer runs when visiting league B parks. To test this claim, a random sample of runs scored by league A teams with and without their DH is given in the accompanying table. Does the designated hitter result in more runs scored at the = 0.05 level of significance? Note that xA = 6.0, sA = 3.5, xB = 4.3, and sB = 2.7. 2 Click the icon to view the data table. Determine the null and alternative hypotheses for this test. A. H0 : A = B H1 : A > B B. H0 : A > B H1 : A = B C. H0 : A = B H1 : A < B D. H0 : A = B H1 : A B Determine the P-value for this test. P-value = (Round to three decimal places as needed.) State the appropriate conclusion. Choose the correct answer below. A. Do not reject H0 . There is sufficient evidence at the level of significance to conclude that games played with a designated hitter result in more runs. B. Reject H0 . There is sufficient evidence at the level of significance to conclude that games played with a designated hitter result in more runs. C. Reject H0 . There is not sufficient evidence at the level of significance to conclude that games played with a designated hitter result in more runs. D. Do not reject H0 . There is not sufficient evidence at the level of significance to conclude that games played with a designated hitter result in more runs. 2: Sample of Runs Full data set League A Park (with DH) 7 2 3 6 8 4 12 5 6 13 1 6 4 6 3 9 3 14 7 5 2 14 6 6 5 7 4 7 5 0 League B Park (without DH) 0 5 5 4 7 8 8 2 10 4 2 3 3 3 6 3 5 5 2 4 1 2 9 1 3 7 2 9 3 2 13. A random sample of 40 adults with no children under the age of 18 years results in a mean daily leisure time of 5.92 hours, with a standard deviation of 2.38 hours. A random sample of 40 adults with children under the age of 18 results in a mean daily leisure time of 4.49 hours, with a standard deviation of 1.58 hours. Construct and interpret a 95% confidence interval for the mean difference in leisure time between adults with no children and adults with children (1 2 ). Let 1 represent the mean leisure hours of adults with no children under the age of 18 and 2 represent the mean leisure hours of adults with children under the age of 18. The 95% confidence interval for (1 2 ) is the range from (Round to two decimal places as needed.) What is the interpretation of this confidence interval? A. There is a 95% probability that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours. B. There is a 95% probability that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours. C. There is 95% confidence that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours. D. There is 95% confidence that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours. hours to hours. 14. A physical therapist wanted to know whether the mean step pulse of men was less than the mean step pulse of women. She randomly selected 55 men and 80 women to participate in the study. Each subject was required to step up and down a 6-inch platform. The pulse of each subject was then recorded. The following results were obtained. Two sample T for Men vs Women N Mean StDev Men 55 112.2 11.2 Women 80 118.8 14.8 99% CI for mu Men mu Women ( 12.51, 0.69) T-Test mu Men = mu Women (vs < ) T = 2.95 P = 0.0019 DF = 131 SE Mean 1.5 1.7 (a) State the null and alternative hypotheses. Which of the following is correct? A. H0 : 1 = 2 ; Ha : 1 < 2 B. H0 : 1 = 2 ; Ha : 1 > 2 C. H0 : 1 = 2 ; Ha : 1 2 (b) Identify the P-value and state the researcher's conclusion if the level of significance was = 0.01. What is the P-value? P-value = State the researcher's conclusion. Which of the following is correct? A. Reject H0 , there is not sufficient evidence to conclude that the mean step pulse of men was less than the mean step pulse of women B. Reject H0 , there is sufficient evidence to conclude that the mean step pulse of men was less than the mean step pulse of women C. Fail to reject H0 , there is sufficient evidence to conclude that the mean step pulse of men was less than the mean step pulse of women D. Fail to reject H0 , there is not sufficient evidence to conclude that the mean step pulse of men was less than the mean step pulse of women (c) What is the 99% confidence interval for the mean difference in pulse rates of men versus women? ( , ) (Use ascending order. Round to two decimal places as needed.) Interpret this result. A. We are 99% confident that the means are in the confidence interval. B. 99% percent of the time the mean difference is in the confidence interval. C. 99% percent of the time the means are in the confidence interval. D. We are 99% confident that the mean difference is in the confidence interval. Student: allan cranford Date: 9/13/16 Instructor: Basu Dipanker Course: MAT-240-Q6622-16EW6 Assignment: 4-2 MyStatLab: Module Four Problem Set 1. A null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. What parameter is being tested? H0 : = 5 H1 : 5 What type of test is being conducted in this problem? Left-tailed test Right-tailed test Two-tailed test What parameter is being tested? Population proportion Population standard deviation Population mean 2. (a) Determine the null and alternative hypotheses, (b) explain what it would mean to make a type I error, and (c) explain what it would mean to make a type II error. Six years ago, 11.6% of registered births were to teenage mothers. A sociologist believes that the percentage has decreased since then. (a) Which of the following is the hypothesis test to be conducted? A. H0 : p = 0.116, H1 : p > 0.116 B. H0 : p = 0.116, H1 : p < 0.116 C. H0 : p = 0.116, H1 : p 0.116 (b) Which of the following is a type I error? A. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 11.6%, when the true percentage is less than 11.6%. B. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 11.6%, when it is the true percentage. C. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 11.6%, when the true percentage is less than 11.6%. (c) Which of the following is a type II error? A. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 11.6%, when the true percentage is less than 11.6%. B. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 11.6%, when it is the true percentage. C. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 11.6%, when it is the true percentage. 3. (a) Determine the null and alternative hypotheses, (b) explain what it would mean to make a type I error, and (c) explain what it would mean to make a type II error. Three years ago, the mean price of a single-family home was $243,750. A real estate broker believes that the mean price has increased since then. (a) Which of the following is the hypothesis test to be conducted? A. H0 : = $243,750; H1 : $243,750 B. H0 : = $243,750; H1 : > $243,750 C. H0 : = $243,750; H1 : < $243,750 (b) Which of the following is a type I error? A. The broker rejects the hypothesis that the mean price is $243,750, when it is the true mean cost. B. The broker fails to reject the hypothesis that the mean price is $243,750, when the true mean price is greater than $243,750. C. The broker rejects the hypothesis that the mean price is $243,750, when the true mean price is greater than $243,750. (c) Which of the following is a type II error? A. The broker fails to reject the hypothesis that the mean price is $243,750, when it is the true mean cost. B. The broker fails to reject the hypothesis that the mean price is $243,750, when the true mean price is greater than $243,750. C. The broker rejects the hypothesis that the mean price is $243,750, when it is the true mean cost. 4. Suppose the null hypothesis is not rejected. State the conclusion based on the results of the test. Six years ago, 12.5% of registered births were to teenage mothers. A sociologist believes that the percentage has decreased since then. Which of the following is the correct conclusion? A. There is not sufficient evidence to conclude that the percentage of teenage mothers has decreased. B. There is sufficient evidence to conclude that the percentage of teenage mothers has remained the same. C. There is not sufficient evidence to conclude that the percentage of teenage mothers has remained the same. D. There is sufficient evidence to conclude that the percentage of teenage mothers has decreased. 5. Suppose the null hypothesis is not rejected. State the conclusion based on the results of the test. Three years ago, the mean price of a single-family home was $243,720. A real estate broker believes that the mean price has decreased since then. Which of the following is the correct conclusion? A. There is not sufficient evidence to conclude that the mean price of a single-family home has not changed. B. There is sufficient evidence to conclude that the mean price of a single-family home has decreased. C. There is sufficient evidence to conclude that the mean price of a single-family home has not changed. D. There is not sufficient evidence to conclude that the mean price of a single-family home has decreased. 6. Determine the critical value for a right-tailed test regarding a population proportion at the = 0.10 level of significance. Click here to view Page 1 of the cumulative standard Normal distribution table.1 Click here to view Page 2 of the cumulative standard Normal distribution table.2 z= (Round to two decimal places as needed.) 1: Cumulative Standard Normal Distribution Table (Page 1) 2: Cumulative Standard Normal Distribution Table (Page 2) 7. Test the hypothesis using the classical approach and the P-value approach. H0 : p = 0.90 versus H1 : p < 0.90 n = 150, x = 125, = 0.05 (a) Perform the test using the classical approach. Choose the correct answer below. There is not enough information to test the hypothesis. Do not reject the null hypothesis. Reject the null hypothesis. (b) Perform the test using the P-value approach. P-value = (Round to four decimal places as needed.) Choose the correct answer below. Do not reject the null hypothesis. Reject the null hypothesis. There is not enough information to test the hypothesis. 8. In a clinical trial, 25 out of 700 patients taking a prescription drug complained of flulike symptoms. Suppose that it is known that 2.1% of patients taking competing drugs complain of flulike symptoms. Is there sufficient evidence to conclude that more than 2.1% of this drug's users experience flulike symptoms as a side effect at the = 0.1 level of significance? What are the null and alternative hypotheses? H0 : p (1) versus H1 : p (2) Use technology to find the P-value. P-value = (Round to three decimal places as needed.) Choose the correct answer below. A. Since P-value < , do not reject the null hypothesis and conclude that there is sufficient evidence that more than 2.1% of the users experience flulike symptoms. B. Since P-value > , do not reject the null hypothesis and conclude that there is not sufficient evidence that more than 2.1% of the users experience flulike symptoms. C. Since P-value > , reject the null hypothesis and conclude that there is not sufficient evidence that more than 2.1% of the users experience flulike symptoms. D. Since P-value < , reject the null hypothesis and conclude that there is sufficient evidence that more than 2.1% of the users experience flulike symptoms. (1) < = > (2) < = > 9. Several years ago, 47% of parents who had children in grades K-12 were satisfied with the quality of education the students receive. A recent poll asked 1,035 parents who have children in grades K-12 if they were satisfied with the quality of education the students receive. Of the 1,035 surveyed, 484 indicated that they were satisfied. Construct a 95% confidence interval to assess whether this represents evidence that parents' attitudes toward the quality of education have changed. What are the null and alternative hypotheses? H0 : p (1) versus H1 : p (2) (Round to two decimal places as needed.) Use technology to find the 95% confidence interval. ( , ) (Round to two decimal places as needed.) What is the correct conclusion? A. Since the interval contains the proportion stated in the null hypothesis, there is sufficient evidence that parents' attitudes toward the quality of education have changed. B. Since the interval does not contain the proportion stated in the null hypothesis, there is sufficient evidence that parents' attitudes toward the quality of education have changed. C. Since the interval contains the proportion stated in the null hypothesis, there is insufficient evidence that parents' attitudes toward the quality of education have changed. D. Since the interval does not contain the proportion stated in the null hypothesis, there is insufficient evidence that parents' attitudes toward the quality of education have changed. (1) > < = (2) > = < 10. In a survey, 42% of the respondents stated that they talk to their pets on the answering machine or telephone. A veterinarian believed this result to be too high, so he randomly selected 250 pet owners and discovered that 90 of them spoke to their pet on the answering machine or telephone. Does the veterinarian have a right to be skeptical? Use the = 0.01 level of significance. What are the null and alternative hypotheses? H0 : p (1) versus H1 : p (2) as needed.) Use technology to find the P-value. P-value = (Round to three decimal places as needed.) Does the veterinarian have a right to be skeptical? A. There is sufficient evidence to conclude that the population proportion of pet owners who talk to their pets on the answering machine or telephone is not 42%. B. There is not sufficient evidence to conclude that the population proportion of pet owners who talk to their pets on the answering machine or telephone is 42%. C. There is sufficient evidence to conclude that the population proportion of pet owners who talk to their pets on the answering machine or telephone is less than 42%. D. There is not sufficient evidence to conclude that the population proportion of pet owners who talk to their pets on the answering machine or telephone is less than 42%. (1) > < = (2) < = > (Round to two decimal places 11. Complete parts (a) through (c) below. (a) Determine the critical value(s) for a right-tailed test of a population mean at the = 0.05 level of significance with 10 degrees of freedom. (b) Determine the critical value(s) for a left-tailed test of a population mean at the = 0.10 level of significance based on a sample size of n = 15. (c) Determine the critical value(s) for a two-tailed test of a population mean at the = 0.10 level of significance based on a sample size of n = 17. 3 Click here to view the t-Distribution Area in Right Tail. (a) tcrit = (1) (Round to three decimal places as needed.) (b) tcrit = (2) (Round to three decimal places as needed.) (c) tcrit = (3) (Round to three decimal places as needed.) 3: t-Distribution Area in Right Tail (1) + (2) + (3) + 12. To test H0 : = 100 versus H1 : 100, a simple random sample size of n = 19 is obtained from a population that is known to be normally distributed. Answer parts (a)-(d). 4 Click here to view the t-Distribution Area in Right Tail. (a) If x = 104.2 and s = 9.1, compute the test statistic. t= (Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the = 0.01 level of significance, determine the critical values. The critical values are . (Use a comma to separate answers as needed. Round to three decimal places as needed.) (c) Draw a t-distribution that depicts the critical region(s). Which of the following graphs shows the critical region(s) in the t-distribution? A. B. C. (d) Will the researcher reject the null hypothesis? A. The researcher will reject the null hypothesis since the test statistic is between the critical values. B. There is not sufficient evidence for the researcher to reject the null hypothesis since the test statistic is not between the critical values. C. The researcher will reject the null hypothesis since the test statistic is not between the critical values. D. There is not sufficient evidence for the researcher to reject the null hypothesis since the test statistic is between the critical values. 4: t-Distribution Area in Right Tail 13. To test H0 : = 20 versus H1 : < 20, a simple random sample of size n = 17 is obtained from a population that is known to be normally distributed. Answer parts (a)-(d). 5 Click here to view the t-Distribution Area in Right Tail. (a) If x = 18.2 and s = 4.4, compute the test statistic. t= (Round to two decimal places as needed.) (b) Draw a t-distribution with the area that represents the P-value shaded. Which of the following graphs shows the correct shaded region? A. B. C. (c) Approximate the P-value. Choose the correct range for the P-value below. A. 0.10 < P-value < 0.15 B. 0.05 < P-value < 0.10 C. 0.20 < P-value < 0.25 D. 0.15 < P-value < 0.20 (d) If the researcher decides to test this hypothesis at the = 0.05 level of significance, will the researcher reject the null hypothesis? A. The researcher will not reject the null hypothesis since the P-value is less than . B. The researcher will reject the null hypothesis since the P-value is not less than . C. The researcher will not reject the null hypothesis since the P-value is not less than . D. The researcher will reject the null hypothesis since the P-value is less than . 5: t-Distribution Area in Right Tail 14. Several years ago, the reported mean age of an inmate on death row was 39.5 years. A sociologist wondered whether the mean age of a death-row inmate has changed since then. She randomly selects 33 death-row inmates and finds that their mean age is 37.7, with a standard deviation of 8.8. Construct a 99% confidence interval about the mean age of death row inmates. What does the interval imply? Choose the correct hypotheses. H0 : (1) H1 : (3) (2) 39.5 (4) 39.5 Construct a 99% confidence interval about the mean age. ( , ) (Use ascending order. Round to two decimal places as needed.) What does the interval imply? A. Since the given mean age is not in the interval, reject the null hypothesis. B. Since the given mean age is in the interval, do not reject the null hypothesis. C. Since the given mean age is not in the interval, do not reject the null hypothesis. D. Since the given mean age is in the interval, reject the null hypothesis. (1) p (2) > = < (3) p (4) < > = 15. It has long been stated that the mean temperature of humans is 98.6F. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6F. They measured the temperatures of 148 healthy adults 1 to 4 times daily for 3 days, obtaining 600 measurements. The sample data resulted in a sample mean of 98.4F and a sample standard deviation of 0.8F. (a)Using the classical approach, judge whether the mean temperature of humans is less than 98.6F at the = 0.01 level of significance. (b)Approximate the P-value. 6 Click here to view the t-Distribution Area in Right Tail. (a) Choose the correct answer below. A. Do not reject H0 since the test statistic is less than the critical value. B. Reject H0 since the test statistic is not less than the critical value. C. Reject H0 since the test statistic is less than the critical value. D. Do not reject H0 since the test statistic is not less than the critical value. (b) The P-value is approximately 6: t-Distribution Area in Right Tail . (Round to four decimal places as needed.) Student: allan cranford Date: 9/13/16 Instructor: Basu Dipanker Course: MAT-240-Q6622-16EW6 Assignment: 4-2 MyStatLab: Module Four Problem Set 1. A null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. What parameter is being tested? H0 : = 5 H1 : 5 What type of test is being conducted in this problem? Left-tailed test Right-tailed test Two-tailed test What parameter is being tested? Population proportion Population standard deviation Population mean 2. (a) Determine the null and alternative hypotheses, (b) explain what it would mean to make a type I error, and (c) explain what it would mean to make a type II error. Six years ago, 11.6% of registered births were to teenage mothers. A sociologist believes that the percentage has decreased since then. (a) Which of the following is the hypothesis test to be conducted? A. H0 : p = 0.116, H1 : p > 0.116 B. H0 : p = 0.116, H1 : p < 0.116 C. H0 : p = 0.116, H1 : p 0.116 (b) Which of the following is a type I error? A. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 11.6%, when the true percentage is less than 11.6%. B. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 11.6%, when it is the true percentage. C. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 11.6%, when the true percentage is less than 11.6%. (c) Which of the following is a type II error? A. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 11.6%, when the true percentage is less than 11.6%. B. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 11.6%, when it is the true percentage. C. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 11.6%, when it is the true percentage. 3. (a) Determine the null and alternative hypotheses, (b) explain what it would mean to make a type I error, and (c) explain what it would mean to make a type II error. Three years ago, the mean price of a single-family home was $243,750. A real estate broker believes that the mean price has increased since then. (a) Which of the following is the hypothesis test to be conducted? A. H0 : = $243,750; H1 : $243,750 B. H0 : = $243,750; H1 : > $243,750 C. H0 : = $243,750; H1 : < $243,750 (b) Which of the following is a type I error? A. The broker rejects the hypothesis that the mean price is $243,750, when it is the true mean cost. B. The broker fails to reject the hypothesis that the mean price is $243,750, when the true mean price is greater than $243,750. C. The broker rejects the hypothesis that the mean price is $243,750, when the true mean price is greater than $243,750. (c) Which of the following is a type II error? A. The broker fails to reject the hypothesis that the mean price is $243,750, when it is the true mean cost. B. The broker fails to reject the hypothesis that the mean price is $243,750, when the true mean price is greater than $243,750. C. The broker rejects the hypothesis that the mean price is $243,750, when it is the true mean cost. 4. Suppose the null hypothesis is not rejected. State the conclusion based on the results of the test. Six years ago, 12.5% of registered births were to teenage mothers. A sociologist believes that the percentage has decreased since then. Which of the following is the correct conclusion? A. There is not sufficient evidence to conclude that the percentage of teenage mothers has decreased. B. There is sufficient evidence to conclude that the percentage of teenage mothers has remained the same. C. There is not sufficient evidence to conclude that the percentage of teenage mothers has remained the same. D. There is sufficient evidence to conclude that the percentage of teenage mothers has decreased. 5. Suppose the null hypothesis is not rejected. State the conclusion based on the results of the test. Three years ago, the mean price of a single-family home was $243,720. A real estate broker believes that the mean price has decreased since then. Which of the following is the correct conclusion? A. There is not sufficient evidence to conclude that the mean price of a single-family home has not changed. B. There is sufficient evidence to conclude that the mean price of a single-family home has decreased. C. There is sufficient evidence to conclude that the mean price of a single-family home has not changed. D. There is not sufficient evidence to conclude that the mean price of a single-family home has decreased. 6. Determine the critical value for a right-tailed test regarding a population proportion at the = 0.10 level of significance. Click here to view Page 1 of the cumulative standard Normal distribution table.1 Click here to view Page 2 of the cumulative standard Normal distribution table.2 z= (Round to two decimal places as needed.) 1: Cumulative Standard Normal Distribution Table (Page 1) 2: Cumulative Standard Normal Distribution Table (Page 2) 7. Test the hypothesis using the classical approach and the P-value approach. H0 : p = 0.90 versus H1 : p < 0.90 n = 150, x = 125, = 0.05 (a) Perform the test using the classical approach. Choose the correct answer below. There is not enough information to test the hypothesis. Do not reject the null hypothesis. Reject the null hypothesis. (b) Perform the test using the P-value approach. P-value = (Round to four decimal places as needed.) Choose the correct answer below. Do not reject the null hypothesis. Reject the null hypothesis. There is not enough information to test the hypothesis. 8. In a clinical trial, 25 out of 700 patients taking a prescription drug complained of flulike symptoms. Suppose that it is known that 2.1% of patients taking competing drugs complain of flulike symptoms. Is there sufficient evidence to conclude that more than 2.1% of this drug's users experience flulike symptoms as a side effect at the = 0.1 level of significance? What are the null and alternative hypotheses? H0 : p (1) versus H1 : p (2) Use technology to find the P-value. P-value = (Round to three decimal places as needed.) Choose the correct answer below. A. Since P-value < , do not reject the null hypothesis and conclude that there is sufficient evidence that more than 2.1% of the users experience flulike symptoms. B. Since P-value > , do not reject the null hypothesis and conclude that there is not sufficient evidence that more than 2.1% of the users experience flulike symptoms. C. Since P-value > , reject the null hypothesis and conclude that there is not sufficient evidence that more than 2.1% of the users experience flulike symptoms. D. Since P-value < , reject the null hypothesis and conclude that there is sufficient evidence that more than 2.1% of the users experience flulike symptoms. (1) < = > (2) < = > 9. Several years ago, 47% of parents who had children in grades K-12 were satisfied with the quality of education the students receive. A recent poll asked 1,035 parents who have children in grades K-12 if they were satisfied with the quality of education the students receive. Of the 1,035 surveyed, 484 indicated that they were satisfied. Construct a 95% confidence interval to assess whether this represents evidence that parents' attitudes toward the quality of education have changed. What are the null and alternative hypotheses? H0 : p (1) versus H1 : p (2) (Round to two decimal places as needed.) Use technology to find the 95% confidence interval. ( , ) (Round to two decimal places as needed.) What is the correct conclusion? A. Since the interval contains the proportion stated in the null hypothesis, there is sufficient evidence that parents' attitudes toward the quality of education have changed. B. Since the interval does not contain the proportion stated in the null hypothesis, there is sufficient evidence that parents' attitudes toward the quality of education have changed. C. Since the interval contains the proportion stated in the null hypothesis, there is insufficient evidence that parents' attitudes toward the quality of education have changed. D. Since the interval does not contain the proportion stated in the null hypothesis, there is insufficient evidence that parents' attitudes toward the quality of education have changed. (1) > < = (2) > = < 10. In a survey, 42% of the respondents stated that they talk to their pets on the answering machine or telephone. A veterinarian believed this result to be too high, so he randomly selected 250 pet owners and discovered that 90 of them spoke to their pet on the answering machine or telephone. Does the veterinarian have a right to be skeptical? Use the = 0.01 level of significance. What are the null and alternative hypotheses? H0 : p (1) versus H1 : p (2) as needed.) Use technology to find the P-value. P-value = (Round to three decimal places as needed.) Does the veterinarian have a right to be skeptical? A. There is sufficient evidence to conclude that the population proportion of pet owners who talk to their pets on the answering machine or telephone is not 42%. B. There is not sufficient evidence to conclude that the population proportion of pet owners who talk to their pets on the answering machine or telephone is 42%. C. There is sufficient evidence to conclude that the population proportion of pet owners who talk to their pets on the answering machine or telephone is less than 42%. D. There is not sufficient evidence to conclude that the population proportion of pet owners who talk to their pets on the answering machine or telephone is less than 42%. (1) > < = (2) < = > (Round to two decimal places 11. Complete parts (a) through (c) below. (a) Determine the critical value(s) for a right-tailed test of a population mean at the = 0.05 level of significance with 10 degrees of freedom. (b) Determine the critical value(s) for a left-tailed test of a population mean at the = 0.10 level of significance based on a sample size of n = 15. (c) Determine the critical value(s) for a two-tailed test of a population mean at the = 0.10 level of significance based on a sample size of n = 17. 3 Click here to view the t-Distribution Area in Right Tail. (a) tcrit = (1) (Round to three decimal places as needed.) (b) tcrit = (2) (Round to three decimal places as needed.) (c) tcrit = (3) (Round to three decimal places as needed.) 3: t-Distribution Area in Right Tail (1) + (2) + (3) + 12. To test H0 : = 100 versus H1 : 100, a simple random sample size of n = 19 is obtained from a population that is known to be normally distributed. Answer parts (a)-(d). 4 Click here to view the t-Distribution Area in Right Tail. (a) If x = 104.2 and s = 9.1, compute the test statistic. t= (Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the = 0.01 level of significance, determine the critical values. The critical values are . (Use a comma to separate answers as needed. Round to three decimal places as needed.) (c) Draw a t-distribution that depicts the critical region(s). Which of the following graphs shows the critical region(s) in the t-distribution? A. B. C. (d) Will the researcher reject the null hypothesis? A. The researcher will reject the null hypothesis since the test statistic is between the critical values. B. There is not sufficient evidence for the researcher to reject the null hypothesis since the test statistic is not between the critical values. C. The researcher will reject the null hypothesis since the test statistic is not between the critical values. D. There is not sufficient evidence for the researcher to reject the null hypothesis since the test statistic is between the critical values. 4: t-Distribution Area in Right Tail 13. To test H0 : = 20 versus H1 : < 20, a simple random sample of size n = 17 is obtained from a population that is known to be normally distributed. Answer parts (a)-(d). 5 Click here to view the t-Distribution Area in Right Tail. (a) If x = 18.2 and s = 4.4, compute the test statistic. t= (Round to two decimal places as needed.) (b) Draw a t-distribution with the area that represents the P-value shaded. Which of the following graphs shows the correct shaded region? A. B. C. (c) Approximate the P-value. Choose the correct range for the P-value below. A. 0.10 < P-value < 0.15 B. 0.05 < P-value < 0.10 C. 0.20 < P-value < 0.25 D. 0.15 < P-value < 0.20 (d) If the researcher decides to test this hypothesis at the = 0.05 level of significance, will the researcher reject the null hypothesis? A. The researcher will not reject the null hypothesis since the P-value is less than . B. The researcher will reject the null hypothesis since the P-value is not less than . C. The researcher will not reject the null hypothesis since the P-value is not less than . D. The researcher will reject the null hypothesis since the P-value is less than . 5: t-Distribution Area in Right Tail 14. Several years ago, the reported mean age of an inmate on death row was 39.5 years. A sociologist wondered whether the mean age of a death-row inmate has changed since then. She randomly selects 33 death-row inmates and finds that their mean age is 37.7, with a standard deviation of 8.8. Construct a 99% confidence interval about the mean age of death row inmates. What does the interval imply? Choose the correct hypotheses. H0 : (1) H1 : (3) (2) 39.5 (4) 39.5 Construct a 99% confidence interval about the mean age. ( , ) (Use ascending order. Round to two decimal places as needed.) What does the interval imply? A. Since the given mean age is not in the interval, reject the null hypothesis. B. Since the given mean age is in the interval, do not reject the null hypothesis. C. Since the given mean age is not in the interval, do not reject the null hypothesis. D. Since the given mean age is in the interval, reject the null hypothesis. (1) p (2) > = < (3) p (4) < > = 15. It has long been stated that the mean temperature of humans is 98.6F. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6F. They measured the temperatures of 148 healthy adults 1 to 4 times daily for 3 days, obtaining 600 measurements. The sample data resulted in a sample mean of 98.4F and a sample standard deviation of 0.8F. (a)Using the classical approach, judge whether the mean temperature of humans is less than 98.6F at the = 0.01 level of significance. (b)Approximate the P-value. 6 Click here to view the t-Distribution Area in Right Tail. (a) Choose the correct answer below. A. Do not reject H0 since the test statistic is less than the critical value. B. Reject H0 since the test statistic is not less than the critical value. C. Reject H0 since the test statistic is less than the critical value. D. Do not reject H0 since the test statistic is not less than the critical value. (b) The P-value is approximately 6: t-Distribution Area in Right Tail . (Round to four decimal places as needed.)