Student: Brandy Freytag Date: 7/19/16 Instructor: Doug LeVeque, Beverly Wood Assignment: MSL Chapter 9 HW Course: MATH_211_1841_May_2016(LeVeque) 1. The distribution of the scores on a certain exam is N(30,5), which means that the exam scores are Normally distributed with a mean of 30 and standard deviation of 5. a. Sketch the curve and label, on the x-axis, the position of the mean, the mean plus or minus one standard deviation, the mean plus or minus two standard deviations, and the mean plus or minus three standard deviations. b. Find the probability that a randomly selected score will be less than 20. Shade the region under the Normal curve whose area corresponds to this probability. a. Choose the correct graph below. A. B. C. 15 20 25 30 35 40 45 15 25 27.5 30 32.5 35 45 25 30 35 40 45 50 55 -3 -2 -3 -2 -3 -2 - + +2 +3 - + +2 +3 - + +2 +3 b. What is the probability that a randomly selected score will be less than 20? Using the Empirical Rule, the probability that a randomly selected score will be less than 20 is about (Type an integer or a decimal.) Which graph shows the distribution with the region shaded under the Normal curve whose area corresponds to the probability that a randomly selected score is less than 20? A. B. C. 15 25 27.5 30 32.5 35 45 15 20 25 30 35 40 45 15 20 25 30 35 40 45 -3 -2 -3 -2 -3 -2 - + +2 +3 - + +2 +3 - + +2 +3 %. 2. A biologist is studying the effects that applying insecticide to a fruit farm has on the local bat population. She collects 23 bats and finds the mean weight of this sample to be 503.4 grams. Assuming the selected bats are a random sample, she concludes that because the sample mean is an unbiased estimator of the population mean, the mean weight of bats in the population is also 503.4 grams. Explain why this is an incorrect interpretation of an unbiased estimator. Why is this an incorrect interpretation of an unbiased estimator? A. Having an "unbiased" estimator means that the mean of the means of all possible samples of the same size would be the same as the population mean. B. Having an "unbiased" estimator means that none of the sample means will be equal to the population mean. C. Having an "unbiased" estimator means that at least two sample means are the same as the population mean. D. Having an "unbiased" estimator means that the sample mean will not be equal to the population mean. 3. The weight of a group of women has a population mean, , of 121 pounds and a population standard deviation, , of 21 pounds. The distribution is right-skewed. Suppose a random sample is taken of 100 of these women's weights. Complete parts a and b below. a. What value should we expect for the mean weight of this sample of 100 women? Why? A. The expected mean weight is about 118.9 pounds, because the sample mean gets smaller with larger sample size. B. The expected mean weight is about 123.1 pounds, because the distribution is right-skewed. C. The expected mean weight is about 121 pounds, because the sample mean is an unbiased estimator of the population mean. D. The expected mean weight is about 123.1 pounds, because the sample mean is an unbiased estimator of the population mean. b. The actual sample mean will not be exactly the value determined in part a. The amount it typically differs from this value is given by the standard error. What is the standard error for a sample mean taken from this population? The standard error of the sample mean is (Type an integer or a decimal.) pounds. 4. One histogram shows the distribution of the length of a certain person's cell phone calls for one month, and the other shows many sample means, in which each is the mean length for 14 randomly selected calls from the same person during that month. Which is which? Explain. Frequency Histogram A 75 60 45 30 15 0 Which is which? Explain. The distribution of the length of this person's cell phone calls for the month is shown in Histogram (1) because this distribution has a (2) standard deviation, and is (3) 3 6 9 12 15 18 Minutes The distribution of many sample means for randomly selected calls from the same person during the month is shown in Histogram (4) because this Frequency Histogram B distribution has a (5) 75 60 45 30 15 0 standard deviation, and is (6) 3 6 9 12 15 18 Minutes (1) B, A, (6) (2) larger smaller skewed in one direction. approximately Normal. (3) skewed in one direction. approximately Normal. (4) B, A, (5) smaller larger 5. The mean age of all 644 used cars for sale in a newspaper one Saturday last month was 7.3 years, with a standard deviation of 6.9 years. The distribution of ages is right-skewed. For a study to determine the reliability of classified ads, a reporter randomly selects 40 of these used cars and plans to visit each owner to inspect the cars. He finds that the mean age of the 40 cars he samples is 7.7 years and the standard deviation of those 40 cars is 5.1 years. Complete parts a through c. a. From the problem statement, which of the values 7.3, 6.9, 7.7, and 5.1 are parameters and which are statistics? The value 7.3 is a (1) The value 6.9 is a (2) The value 7.7 is a (3) The value 5.1 is a (4) b. Find , , s, and x. = = s= x= (Type integers or decimals.) c. Are the conditions for using the CLT (Central Limit Theorem) fulfilled? A. No, because the Normal condition is not fulfilled. B. No, because the random sample/independence condition is not fulfilled. C. No, because the random sample/independence and Normal conditions are not fulfilled. D. Yes, all the conditions for using the CLT are fulfilled. What would be the shape of the approximate sampling distribution of a large number of means, each from a sample of 40 cars? Normal Uniform Left-skewed Right-skewed The shape cannot be determined. (1) statistic. parameter. (2) parameter. statistic. (3) statistic. parameter. (4) statistic. parameter. 6. A random sample of 35 students taking statistics at a community college was asked their GPA. The sample mean was 3.44, and the margin of error for a 95% confidence interval was 0.24. Complete parts a and b below. a. Choose the correct interpretation of the confidence interval below and fill in the answer boxes to complete your choice. Assume that the conditions for constructing a confidence interval are met. A. We are 95% confident that the population mean GPA for all of the students in the school is between and . B. We are 95% confident that the population mean GPA of statistics students at the school is between and . C. We are 95% confident that the recorded sample mean GPA of statistics students at the school is between and . (Type integers or decimals rounded to the nearest hundredth as needed. Use ascending order.) b. What does the interval tell us about the population mean GPA for statistics students at the school? Can you reject 2.51 as the mean for statistics students? Explain. A. It tells us a range of plausible values for the population mean GPA, where the population is all statistics students at the school. Yes, reject 2.51, because it is not in the interval. We are confident that the statistics students have a higher population mean than 2.51. B. It tells us a range of plausible values for the population mean GPA, where the population is all students at the school. Yes, reject 2.51, because it is not in the interval. We are confident that all students have a higher population mean than 2.51. C. It tells us a range of plausible values for the sample mean GPA. Yes, reject 2.51, because it is not in the interval. We are confident that the statistics students have a higher population mean than 2.51. D. It tells us a range of plausible values for the population mean GPA, where the population is all statistics students at the school. No, do not reject 2.51, because it is within the interval. 7. A statistics instructor randomly selected four bags of oranges, each bag labeled 10 pounds, and weighed the bags. They weighed 10.4, 10.4, 10.8, and 10.4 pounds. Assume that the distribution of weights is Normal. Find a 95% confidence interval for the mean weight of all bags of oranges. Use technology for your calculations. Answer parts a and b below. a. Choose the correct interpretation of the confidence interval below and, if necessary, fill in the answer boxes to complete your choice. A. There is a 95% chance that all intervals will be between B. We are 95% confident the population mean is between and and C. We are 95% confident that the sample mean is between and . . . D. The requirements for constructing a confidence interval are not satisfied. (Type integers or decimals rounded to the nearest thousandth as needed. Use ascending order.) b. Does the interval capture 10 pounds? Is there enough evidence to reject the null hypothesis that the population mean weight is 10 pounds? Explain your answer. A. Yes, it does capture 10. Do not reject the claim of 10 pounds because 10 is in the interval. B. Yes, it does capture 10. Reject the claim of 10 pounds because 10 is in the interval. C. No, it does not capture 10. Do not reject the claim of 10 pounds because 10 is not in the interval. D. No, it does not capture 10. Reject the claim of 10 pounds because 10 is not in the interval. 8. A random sample of 28 independent female college-aged dancers showed a sample mean height of 62.6 inches and a sample standard deviation of 1.7 inches. Assume that this distribution of heights is Normal. Complete parts a through c below. a. Use technology to find a 95% confidence interval for the population mean height of dancers and interpret the interval. Choose the correct answer below and, if necessary, fill in the answer boxes to complete your choice. A. We are 95% confident that the sample mean height of female college-aged dancers is between and . B. We are 95% confident that the population mean height of all dancers is between and . C. We are 95% confident that the population mean height of female college-aged dancers is between and . D. The requirements for constructing a confidence interval are not satisfied. (Type integers or decimals rounded to the nearest tenth as needed. Use ascending order.) b. Use technology to find a 99% confidence interval for the population mean height and interpret the interval. Choose the correct answer below and, if necessary, fill in the answer boxes to complete your choice. A. We are 99% confident that the population mean height of female college-aged dancers is between and . B. We are 99% confident that the population mean height of all dancers is between and . C. We are 99% confident that the sample mean height of female college-aged dancers is between and . D. The requirements for constructing a confidence interval are not satisfied. (Type integers or decimals rounded to the nearest tenth as needed. Use ascending order.) c. Which interval is wider and why? A. The 99% interval is wider because it has a greater confidence level, and therefore we use a smaller value of t*, which creates a wider interval. B. The 95% interval is wider because it has a lower confidence level, and therefore we use a smaller value of t*, which creates a wider interval. C. The 95% interval is wider because it has a lower confidence level, and therefore we use a bigger value of t*, which creates a wider interval. D. The 99% interval is wider because it has a greater confidence level, and therefore we use a bigger value of t*, which creates a wider interval. 9. State whether each of the following changes would make a confidence interval wider or narrower. (Assume that nothing else changes.) a. Changing from a 99% confidence level to a 90% confidence level. b. Changing from a sample size of 200 to a sample size of 30. c. Changing from a standard deviation of 25 pounds to a standard deviation of 15 pounds. 1 Click the icon to view the t-table. a. How will changing from a 99% confidence level to a 90% confidence level affect the width of the confidence interval? A. The interval will become wider. B. The interval will become narrower. C. This change will not affect the width of the interval. b. How will changing from a sample size of 200 to a sample size of 30 affect the width of the confidence interval? A. The interval will become narrower. B. The interval will become wider. C. This change will not affect the width of the interval. c. How will changing from a standard deviation of 25 pounds to a standard deviation of 15 pounds affect the width of the confidence interval? A. The interval will become wider. B. The interval will become narrower. C. This change will not affect the width of the interval. 1: t-table 10. Thirty GPAs from a randomly selected sample of statistics students at a college are linked below. Assume that the population distribution is approximately Normal. The technician in charge of records claimed that the population mean GPA for the whole college is 2.84. a. What is the sample mean? Is it higher or lower than the population mean of 2.84? b. The chair of the mathematics department claims that statistics students typically have higher GPAs than the typical college student. Use the four-step procedure and the data provided to test this claim. Use a significance level of 0.05. 2 Click the icon to view the data table. a. What is the sample mean? The sample mean is . (Type an integer or decimal rounded to two decimal places as needed.) Is the sample mean higher or lower than the population mean of 2.84? The sample mean is (1) than the population mean of 2.84. b. The chair of the mathematics department claims that statistics students typically have higher GPAs than the typical college student. Use the four-step procedure and the data provided to test this claim. Use a significance level of 0.05. Which of the following correctly states H0 and Ha ? A. D. H0 : 2.84 B. Ha : = 2.84 H0 : = 2.84 E. Ha : 2.84 H0 : = 2.84 C. Ha : > 2.84 H0 : = 2.84 F. Ha : < 2.84 H0 : > 2.84 Ha : 2.84 H0 : 2.84 Ha : < 2.84 Find the test statistic. t= (Type an integer or decimal rounded to two decimal places as needed.) Find the p-value. p= (Type an integer or decimal rounded to three decimal places as needed.) Reject or do not reject H0 . Choose the correct answer below. A. Reject H0 . The mean GPA for statistics students is significantly higher than 2.84. B. Reject H0 . The mean GPA for statistics students is significantly lower than 2.84. C. Do not reject H0 . The mean GPA for statistics students is not significantly higher than 2.84. D. Do not reject H0 . The mean GPA for statistics students is definitely 2.84. 2: Student GPA Table 2.81 2.84 3.03 (1) 3.37 2.69 3.04 3.18 3.52 3.15 2.58 3.02 2.99 3.43 2.76 3.44 2.78 3.48 3.89 3.04 2.41 2.55 3.53 3.16 3.15 2.64 3.43 3.17 3.91 3.16 3.08 higher lower 11. A random and independently chosen sample of four bags of horse carrots, each bag labeled 20 pounds, had weights of 20.1, 19.6, 20.7, and 20.0 pounds. Assume that the distribution of weights in the population is Normal. Complete parts a through c below. a. Test the hypothesis that the population mean weight is not 20 pounds. Which of the following correctly states H0 and Ha ? A. D. H0 : = 20 Ha : < 20 H0 : = 20 Ha : 20 B. E. H0 : 20 Ha : = 20 H0 : > 20 Ha : 20 C. F. H0 : 20 Ha : < 20 H0 : = 20 Ha : > 20 Find the test statistic. t= (Type an integer or decimal rounded to two decimal places as needed.) Find the p-value. p= (Type an integer or decimal rounded to three decimal places as needed.) Reject or do not reject H0 . Choose the correct answer below. A. Do not reject H0 . There is no reason to believe that the population mean is not 20 pounds on the basis of these data at a significance level of 0.05. B. Reject H0 . There is no reason to believe that the population mean is not 20 pounds on the basis of these data at a significance level of 0.05. C. Reject H0 . There is reason to believe that the population mean is not 20 pounds on the basis of these data at a significance level of 0.05. D. Do not reject H0 . There is reason to believe that the population mean is not 20 pounds on the basis of these data at a significance level of 0.05. b. Test the hypothesis that the population mean is less than 20 pounds. Which of the following correctly states H0 and Ha ? A. D. H0 : > 20 Ha : 20 H0 : 20 Ha : = 20 B. E. H0 : = 20 Ha : > 20 H0 : = 20 Ha : 20 Find the test statistic. t= (Type an integer or decimal rounded to two decimal places as needed.) Find the p-value. p= (Type an integer or decimal rounded to three decimal places as needed.) Reject or do not reject H0 . Choose the correct answer below. C. F. H0 : = 20 Ha : < 20 H0 : 20 Ha : < 20 A. Do not reject H0 . There is no reason to believe that the population mean is less than 20 pounds on the basis of these data at a significance level of 0.05. B. Reject H0 . There is reason to believe that the population mean is less than 20 pounds on the basis of these data at a significance level of 0.05. C. Do not reject H0 . There is reason to believe that the population mean is less than 20 pounds on the basis of these data at a significance level of 0.05. D. Reject H0 . There is no reason to believe that the population mean is less than 20 pounds on the basis of these data at a significance level of 0.05. c. Test the hypothesis that the population mean is more than 20 pounds. Which of the following correctly states H0 and Ha ? A. D. H0 : = 20 Ha : < 20 H0 : 20 Ha : = 20 B. E. H0 : = 20 Ha : 20 H0 : 20 Ha : < 20 C. F. H0 : = 20 Ha : > 20 H0 : > 20 Ha : 20 Find the test statistic. t= (Type an integer or decimal rounded to two decimal places as needed.) Find the p-value. p= (Type an integer or decimal rounded to three decimal places as needed.) Reject or do not reject H0 . Choose the correct answer below. A. Reject H0 . There is reason to believe that the population mean is more than 20 pounds on the basis of these data at a significance level of 0.05. B. Do not reject H0 . There is no reason to believe that the population mean is more than 20 pounds on the basis of these data at a significance level of 0.05. C. Reject H0 . There is no reason to believe that the population mean is more than 20 pounds on the basis of these data at a significance level of 0.05. D. Do not reject H0 . There is reason to believe that the population mean is more than 20 pounds on the basis of these data at a significance level of 0.05. 12. Suppose that 400 statistics students each took a random sample (with replacement) of 100 students at their college and recorded the ages of the students in their sample. Then each student used his or her data to calculate a 95% confidence interval for the mean age of all students at the college. How many of the 400 intervals would you expect to capture the true population mean age, and how many would you expect not to capture the true population mean? Explain by showing your calculation. The number of intervals expected to capture the true population mean is (Type an integer or a decimal.) The number of intervals expected to not capture the true population mean is (Type an integer or a decimal.) The expression (1) population mean. (1) 0.95(400) 95(400) 400 0.95 400 95 . . can be used to find the number of intervals expected to capture the true 13. Triglycerides are a form of fat found in the body. A recent study looked at whether men have higher triglyceride levels than women. After the data were collected, Minitab was used to find a 95% confidence interval for the difference between the mean triglyceride levels for men and women. The Minitab output is provided. Complete parts a and b below. 3 Click the icon to view the Minitab output. a. Report and interpret the 95% confidence interval for the difference in mean triglycerides between men and women (refer to the Minitab output provided). Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice. (Type integers or decimals.) A. The difference in mean triglycerides between men and women is definitely between and B. The difference in mean triglycerides between men and women is definitely . . C. It can be stated with 95% confidence that the difference in mean triglycerides between men and women is between and . D. There is a 95% chance that the difference in mean triglycerides between men and women is between and . b. Does this support the hypothesis that men and women differ in mean triglyceride levels? Explain. Because the interval (1) contain zero, the possibility that the mean difference in the population is 0 be ruled out. Since this difference, female male , (3) (2) triglyceride level is (4) the men's mean the women's mean triglyceride level. 3: Minitab output for the 95% confidence interval Two-sample T-Test and CI: Triglycerides, Gender Gender Female Male N 41 44 Mean 92.7 139.8 StDev 46.2 60.5 SE Mean 7.2 9.1 Difference = mu (Female) mu (Male) Estimate for difference: 47.1 95% CI for difference: ( 70.2, 24.0) (1) does does not (2) cannot can (3) is negative, (4) significantly higher than is positive, significantly lower than could be zero, not significantly different from 14. In a study, 120 rental properties that had already been the target of drug law enforcement were randomly divided into two groups. In the experimental group, the tenants received a letter from the police describing the enforcement tactics in place. For the control group, there was no letter. The table gives summary statistics for the number of crimes reported over a 30-month interval. Determine whether the letter from the police was effective in reducing the number of crimes at the 0.05 level. Although the distribution of number of crimes is not Normal, assume that the sample size is large enough for the Central Limit Theorem to apply. Mean SD n Experimental 3.7 4.1 80 Control 5.7 6.1 40 Determine the hypotheses for this test. Let L be the population mean number of crimes reported over a 30-month interval for properties that received a letter from the police, and let N be the population mean number of crimes reported over a 30-month interval for properties that did not receive a letter. Choose the correct answer below. A. H0 : L = N Ha : L N B. H0 : L = N Ha : L < N C. H0 : L > N Ha : L = N D. H0 : L N Ha : L = N E. H0 : L = N Ha : L > N F. H0 : L < N Ha : L = N Find the test statistic for this test. t= (Round to two decimal places as needed.) Find the p-value for this test. p-value = (Round to three decimal places as needed.) What is the conclusion for this test? A. Do not reject H0 . The letter from the police was not significantly effective in reducing the number of crimes. B. Reject H0 . The letter from the police was not significantly effective in reducing the number of crimes. C. Reject H0 . The letter from the police was significantly effective in reducing the number of crimes. D. Do not reject H0 . The letter from the police was significantly effective in reducing the number of crimes. 15. The prices of a sample of books at University A were obtained by two statistics students. Then the cost of books for the same subjects (at the same level) were obtained for University B. Assume that the distribution of differences is Normal enough to proceed, and assume that the sampling was random. a. First find both sample means and compare them. b. Test the hypothesis that the population means are different, using a significance level of 0.05. 4 Click the icon to view the table of prices. a. Find the sample mean for University A. $ (Round to the nearest cent as needed.) Find the sample mean for University B. $ (Round to the nearest cent as needed.) Compare the sample means. The sample mean is larger at (1) b. Determine the hypotheses for this test. Let difference be the mean of differences between the paired observations. Choose the correct answer below. A. H0 : difference = 0 Ha : difference > 0 B. H0 : difference = 0 Ha : difference < 0 C. H0 : difference < 0 Ha : difference = 0 D. H0 : difference 0 Ha : difference = 0 E. H0 : difference > 0 Ha : difference = 0 F. H0 : difference = 0 Ha : difference 0 Find the test statistic for this test. t= (Round to two decimal places as needed.) Find the p-value for this test. p-value = (Round to three decimal places as needed.) What is the conclusion for this test? A. Do not reject H0 . There is evidence that mean of the differences is not 0. B. Reject H0 . There is evidence that mean of the differences is not 0. C. Reject H0 . There is not evidence that mean of the differences is not 0. D. Do not reject H0 . There is not evidence that mean of the differences is not 0. 4: Data Table University A ($) 44 62 57 78 83 86 87 41 70 54 88 84 88 77 44 (1) University B ($) 58 76 68 77 89 93 81 43 74 47 98 89 101 81 51 University B. University A. 16. Data for the ages of grooms and their brides for a random sample of 31 couples in a certain county are provided. Complete parts a through c below. 5 Click the icon to view the data. a. Find and compare the sample means. The sample mean for the grooms, , is (1) than the sample mean for their brides, . ( Round to three decimal places as needed.) b. Test the hypothesis that there is a significant difference in mean ages of brides and grooms, using a significance level of 0.05. Determine the hypotheses for this test. Let difference be the population mean difference between the ages of grooms and their brides, in years. Choose the correct answer below. A. H0 : difference = 0 Ha : difference > 0 B. H0 : difference 0 Ha : difference < 0 C. H0 : difference 0 Ha : difference > 0 D. H0 : difference 0 Ha : difference = 0 E. H0 : difference = 0 Ha : difference 0 F. H0 : difference = 0 Ha : difference < 0 Find the test statistic for this test. t= (Round to two decimal places as needed.) Find the p-value for this test. p-value = (Round to three decimal places as needed.) What is the conclusion for this test? A. Do not reject H0 . The mean ages are not significantly different. B. Do not reject H0 . The mean ages are significantly different. C. Reject H0 . The mean ages are significantly different. D. Reject H0 . The mean ages are not significantly different. c. If the test had been done to determine whether the mean for the grooms was significantly larger than the mean for the brides, how would that change the alternative hypothesis and the p-value? What would the alternative hypothesis become? A. Ha : difference = 0 B. Ha : difference > 0 C. Ha : difference 0 D. Ha : difference < 0 How would the p-value change? A. The new p-value would be half of the p-value from the test performed above. B. The new p-value would be twice the p-value from the test performed above. C. The new p-value would be the p-value from the test performed above subtracted from 1. D. The p-value would not change. 5: Data Table Age (years) Groom Bride 22 25 33 29 23 23 26 20 30 32 23 24 34 37 42 42 27 21 47 47 26 26 (1) Age (years) Groom Bride 27 23 22 20 17 20 28 23 23 26 23 23 22 22 20 20 28 26 28 23 Full Data Set Age (years) Groom Bride 30 27 15 18 28 22 26 25 32 27 25 23 26 27 27 29 22 22 25 26 greater less 17. A random sample of students at a college reported what they believed to be their heights in inches. Then the students measured each others' heights in centimeters, without shoes. The data provided are for the men, with their believed heights converted from inches to centimeters. Assume that conditions for t-tests hold. Complete parts a and b below. 6 Click the icon to view the data. a. Find a 95% confidence interval for the mean difference as measured in centimeters. Does it capture 0? What does that show? The 95% confidence interval is ( (Round to three decimal places as needed.) The interval (1) rejected. , ). include 0, so a hypothesis that the means are equal (2) be b. Perform a t-test to test the hypothesis that the means are not the same. Use a significance level of 0.05. Determine the hypotheses for this test. Let difference be the population mean difference between measured and believed height, in centimeters. Choose the correct answer below. A. H0 : difference 0 Ha : difference < 0 B. H0 : difference = 0 Ha : difference > 0 C. H0 : difference = 0 Ha : difference 0 D. H0 : difference 0 Ha : difference = 0 E. H0 : difference 0 Ha : difference > 0 F. H0 : difference = 0 Ha : difference < 0 Find the test statistic for this test. t= (Round to two decimal places as needed.) Find the p-value for this test. p-value = (Round to three decimal places as needed.) What is the conclusion for this test? A. Reject H0 . The means of measured and believed heights are significantly different. B. Do not reject H0 . The means of measured and believed heights are not significantly different. C. Do not reject H0 . The means of measured and believed heights are significantly different. D. Reject H0 . The means of measured and believed heights are not significantly different. 6: Data Table Full Data Set Men Centimeters Centimeters (measured) (believed) 179 180.34 175 177.80 181 180.34 177 177.80 170 167.64 170 172.72 183 180.34 Men Centimeters Centimeters (measured) (believed) 164 165.10 172 175.26 184 182.88 164 172.72 193 190.50 175 175.26 172 172.72 191 195.58 (1) does not (2) can does cannot 18. Two surfers and statistics students collected data on the number of days on which surfers surfed in the last month for 30 longboard (L) users and 30 shortboard (S) users. Treat these data as though they were from two independent random samples. Test the hypothesis that the mean days surfed for all longboarders is larger than the mean days surfed for all shortboarders (because longboards can go out in many different surfing conditions). Use a level of significance of 0.05. Longboard: 15,6,11,6,20,11,12,12,12,19,8,6,19,11,7,15,6,8,15,8,6,14,5,19,9,11,13,22,13,9 Shortboard: 19,7,6,8,7,6,7,4,17,7,5,5,19,4,16,5,16,3,10,9,6,7,3,3,12,7,6,18,10,19 Determine the hypotheses for this test. Choose the correct answer below. A. H0 : L < S Ha : L = S B. H0 : L = S Ha : L < S C. H0 : L S Ha : L = S D. H0 : L = S Ha : L S E. H0 : L > S Ha : L = S F. H0 : L = S Ha : L > S Find the test statistic for this test. t= (Round to two decimal places as needed.) Find the p-value for this test. p-value = (Round to three decimal places as needed.) What is the conclusion for this test? A. Do not reject H0 . The mean days surfed for longboarders is significantly larger than the mean days surfed for all shortboarders B. Do not reject H0 . The mean days surfed for longboarders is not significantly larger than the mean days surfed for all shortboarders C. Reject H0 . The mean days surfed for longboarders is not significantly larger than the mean days surfed for all shortboarders D. Reject H0 . The mean days surfed for longboarders is significantly larger than the mean days surfed for all shortboarders 19. Eric randomly surveyed 150 adults from a certain city and asked which team in a contest they were rooting for, either North High School or South High School. Of the surveyed adults, 96 said they were rooting for North High while the rest said they were rooting for South High. Eric wants to determine if this is evidence that more than half the adults in this city will root for North High School. Suppose a p-value from the correct hypothesis test was 0.0030. Which of the following is a correct interpretation of this p-value? Choose the correct answer below. A. There's a 0.3% chance that the null hypothesis is true. B. It states that 3 out of every 1000 random samples of the same size from this population would produce the same result observed in this study or a result more unusual. C. If half of all adults in this city root for North High, 3 out of every 1000 random samples of the same size from this population would produce the same result observed in this study or a result more unusual. D. If more than half of all adults in this city root for North High, 3 out of every 1000 random samples of the same size from this population would produce the same result observed in this study or a result more unusual. 20. It is recommended that adults get 8 hours of sleep each night. A researcher hypothesized college students got less than the recommended number of hours of sleep each night, on average. The researcher randomly sampled 20 college students and found no evidence to reject the null hypothesis at the 5% significance level. What is true regarding the p-value from this hypothesis test? Choose the correct answer below. A. The p-value must have been greater than 0.05. B. The p-value must have been equal to 0.05. C. The p-value must have been less than or equal to 0.05. D. We cannot determine a range for the p-value based on the information given. 21. Match each description with the correct histogram of the data. 1. The age of death of a sample of 19 typical women in the U.S. 2. The yearly tuition for 142 colleges, 85 of which are private and 57 of which are state-supported. 3. The outcomes of rolling a fair die (with six sides) 5000 times. C Frequency B Frequency Frequency A What is the correct way to match the descriptions to the histograms? A. 1B, 2C, 3A B. 1B, 2A, 3C C. 1A, 2B, 3C D. 1C, 2A, 3B Frequency 22. A sample of thirty users of a popular social networking site yielded the histogram on the right for the number of friends. What is the relationship between the mean and the median for this data? 14 12 10 8 6 4 2 0 50 100 150 200 250 300 350 Number of Friends Choose the correct answer below. A. The mean will be substantially smaller than the median since the distribution is skewed left. B. The mean and median will be roughly equal since the distribution is fairly symmetric. C. The mean will be substantially smaller than the median since the distribution is skewed right. D. The mean will be substantially larger than the median since the distribution is skewed right. 23. Identify when the interquartile range is better than the standard deviation as a measure of dispersion and explain its advantage. Choose the correct answer below. A. When the distribution is symmetric, then the interquartile range is preferred since it is easier to calculate. B. When the distribution is skewed left or right or contains some extreme observations, then the interquartile range is preferred since it uses all the observations in its calculation. C. When the distribution is symmetric, then the interquartile range is preferred since it is resistant. D. When the distribution is skewed left or right or contains some extreme observations, then the interquartile range is preferred since it is resistant