Probablitiy QNT/351 Version 5 University of Phoenix Material PROBABILITY Maximum and Minimum Temperatures Search the Internet for U.S. climate data. Choose the city in which you live. Click on the tab that reads \"Daily.\" 1. Prepare a spreadsheet with three columns: Date, High Temperature, and Low Temperature. List the past 60 days for which data is available. 2. Prepare a histogram for the data on high temperatures and comment on the shape of the distribution as observed from these graphs. 3. Calculate and S. 4. What percentage of the high temperatures are within the interval - S to + S? 5. What percentage of the high temperatures are within the interval - 2S to + 2S? 6. How do these percentages compare to the corresponding percentages for a normal distribution (68.26% and 95.44%, respectively)? 7. Repeat Parts 2 to 6 for the minimum temperatures on your spreadsheet. 8. Would you conclude that the two distributions are normally distributed? Why or why not? Copyright 2016 by University of Phoenix. All rights reserved. 1 A sample of 35 observations is selected from a normal population. The sample mean is 26, and the population standard deviation is 4. Conduct the following test of hypothesis using the 0.05 significance level. H0 : 25 H1 : > 25 a. Is this a one- or two-tailed test? "Two-tailed"-the alternate hypothesis is different from direction. "One-tailed"-the alternate hypothesis is greater than direction. b. What is the decision rule? (Round your answer to 3 decimal places.) H0, when z > (Click to select) c. What is the value of the test statistic? (Round your answer to 2 decimal places.) Value of the test statistic d. What is your decision regarding H0? Do not reject Reject There is evidence to conclude that the population mean is greater than 25. (Click to select) e. What is the p-value? (Round your answer to 4 decimal places.) p-value At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, \"You can average $72 a day in tips.\" Assume the population of daily tips is normally distributed with a standard deviation of $2.45. Over the first 34 days she was employed at the restaurant, the mean daily amount of her tips was $73.07. At the 0.10 significance level, can Ms. Brigden conclude that her daily tips average more than $72? a. State the null hypothesis and the alternate hypothesis. H0: >72 ; H1: = 72 H0: = 72 ; H1: 72 H0: 72 ; H1: < 72 H0: 72 ; H1: > 72 b. State the decision rule. Reject H1 if z < 1.28 Reject H1 if z > 1.28 Reject H0 if z > 1.28 Reject H0 if z < 1.28 c. Compute the value of the test statistic. (Round your answer to 2 decimal places.) Value of the test statistic d. What is your decision regarding H0? Do not reject H0 Reject H0 e. What is the p-value? (Round your answer to 4 decimal places.) p-value The Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales representatives make an average of 40 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 38 sales representatives reveals that the mean number of calls made last week was 41. The standard deviation of the sample is 2.6 calls. Using the 0.025 significance level, can we conclude that the mean number of calls per salesperson per week is more than 40? H0 : 40 H1 : > 40 1. Compute the value of the test statistic. (Round your answer to 3 decimal places.) Value of the test statistic 2. What is your decision regarding H0? H0. The mean number of calls is (Click to select) than 40 per week. (Click to select) A United Nations report shows the mean family income for Mexican migrants to the United States is $27,150 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 30 Mexican family units reveals a mean to be $29,500 with a sample standard deviation of $11,150. Does this information disagree with the United Nations report? Apply the 0.01 significance level. a. State the null hypothesis and the alternate hypothesis. H0: = H1: b. State the decision rule for .01 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) Reject H0 if t is not between and c. Compute the value of the test statistic. (Round your answer to 2 decimal places.) Value of the test statistic d. Does this information disagree with the United Nations report? Apply the 0.01 significance level. . This data (Click to select) the report. (Click to select) The following information is available. H0 : 220 H1 : < 220 A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the .025 significance level. a. Is this a one- or two-tailed test? One-tailed test Two-tailed test b. What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) H0 when z < (Click to select) c. What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) Value of the test statistic d. What is your decision regarding H0? Reject Do not reject e. What is the p-value? (Round your answer to 4 decimal places.) p-value Given the following hypotheses: H0 : 10 H1 : > 10 A random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation 3. Using the .05 significance level: a. State the decision rule. (Round your answer to 3 decimal places.) Reject H0 if t > b. Compute the value of the test statistic. (Round your answer to 3 decimal places.) Value of the test statistic c. What is your decision regarding the null hypothesis? H0. There is (Click to select) evidence to conclude that the (Click to select) population mean is greater than 10. Given the following hypotheses: H0 : = 400 H1 : 400 A random sample of 12 observations is selected from a normal population. The sample mean was 407 and the sample standard deviation 6. Using the .01 significance level: a. State the decision rule. (Negative amount should be indicated by a minus sign. Round your answers to 3 decimal places.) Reject H0 when the test statistic is the interval ( (Click to select) b. Compute the value of the test statistic. (Round your answer to 3 decimal places.) , ). Value of the test statistic c. What is your decision regarding the null hypothesis? Do not reject A sample of 35 observations is selected from a normal population. The sample mean is 26, and the population standard deviation is 4. Conduct the following test of hypothesis using the 0.05 significance level. H0 : 25 H1 : > 25 a. Is this a one- or two-tailed test? "Two-tailed"-the alternate hypothesis is different from direction. "One-tailed"-the alternate hypothesis is greater than direction. b. What is the decision rule? (Round your answer to 3 decimal places.) H0, when z > (Click to select) c. What is the value of the test statistic? (Round your answer to 2 decimal places.) Value of the test statistic d. What is your decision regarding H0? Do not reject Reject There is evidence to conclude that the population mean is greater than 25. (Click to select) e. What is the p-value? (Round your answer to 4 decimal places.) p-value At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, \"You can average $72 a day in tips.\" Assume the population of daily tips is normally distributed with a standard deviation of $2.45. Over the first 34 days she was employed at the restaurant, the mean daily amount of her tips was $73.07. At the 0.10 significance level, can Ms. Brigden conclude that her daily tips average more than $72? a. State the null hypothesis and the alternate hypothesis. H0: >72 ; H1: = 72 H0: = 72 ; H1: 72 H0: 72 ; H1: < 72 H0: 72 ; H1: > 72 b. State the decision rule. Reject H1 if z < 1.28 Reject H1 if z > 1.28 Reject H0 if z > 1.28 Reject H0 if z < 1.28 c. Compute the value of the test statistic. (Round your answer to 2 decimal places.) Value of the test statistic d. What is your decision regarding H0? Do not reject H0 Reject H0 e. What is the p-value? (Round your answer to 4 decimal places.) p-value The Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales representatives make an average of 40 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 38 sales representatives reveals that the mean number of calls made last week was 41. The standard deviation of the sample is 2.6 calls. Using the 0.025 significance level, can we conclude that the mean number of calls per salesperson per week is more than 40? H0 : 40 H1 : > 40 1. Compute the value of the test statistic. (Round your answer to 3 decimal places.) Value of the test statistic 2. What is your decision regarding H0? H0. The mean number of calls is (Click to select) than 40 per week. (Click to select) A United Nations report shows the mean family income for Mexican migrants to the United States is $27,150 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 30 Mexican family units reveals a mean to be $29,500 with a sample standard deviation of $11,150. Does this information disagree with the United Nations report? Apply the 0.01 significance level. a. State the null hypothesis and the alternate hypothesis. H0: = H1: b. State the decision rule for .01 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) Reject H0 if t is not between and c. Compute the value of the test statistic. (Round your answer to 2 decimal places.) Value of the test statistic d. Does this information disagree with the United Nations report? Apply the 0.01 significance level. . This data (Click to select) the report. (Click to select) The following information is available. H0 : 220 H1 : < 220 A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the .025 significance level. a. Is this a one- or two-tailed test? One-tailed test Two-tailed test b. What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) H0 when z < (Click to select) c. What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) Value of the test statistic d. What is your decision regarding H0? Reject Do not reject e. What is the p-value? (Round your answer to 4 decimal places.) p-value Given the following hypotheses: H0 : 10 H1 : > 10 A random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation 3. Using the .05 significance level: a. State the decision rule. (Round your answer to 3 decimal places.) Reject H0 if t > b. Compute the value of the test statistic. (Round your answer to 3 decimal places.) Value of the test statistic c. What is your decision regarding the null hypothesis? H0. There is (Click to select) evidence to conclude that the (Click to select) population mean is greater than 10. Given the following hypotheses: H0 : = 400 H1 : 400 A random sample of 12 observations is selected from a normal population. The sample mean was 407 and the sample standard deviation 6. Using the .01 significance level: a. State the decision rule. (Negative amount should be indicated by a minus sign. Round your answers to 3 decimal places.) Reject H0 when the test statistic is the interval ( (Click to select) b. Compute the value of the test statistic. (Round your answer to 3 decimal places.) , ). Value of the test statistic c. What is your decision regarding the null hypothesis? Do not reject A sample of 35 observations is selected from a normal population. The sample mean is 26, and the population standard deviation is 4. Conduct the following test of hypothesis using the 0.05 significance level. H0 : 25 H1 : > 25 a. Is this a one- or two-tailed test? "Two-tailed"-the alternate hypothesis is different from direction. "One-tailed"-the alternate hypothesis is greater than direction. b. What is the decision rule? (Round your answer to 3 decimal places.) H0, when z > (Click to select) c. What is the value of the test statistic? (Round your answer to 2 decimal places.) Value of the test statistic d. What is your decision regarding H0? Do not reject Reject There is evidence to conclude that the population mean is greater than 25. (Click to select) e. What is the p-value? (Round your answer to 4 decimal places.) p-value At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, \"You can average $72 a day in tips.\" Assume the population of daily tips is normally distributed with a standard deviation of $2.45. Over the first 34 days she was employed at the restaurant, the mean daily amount of her tips was $73.07. At the 0.10 significance level, can Ms. Brigden conclude that her daily tips average more than $72? a. State the null hypothesis and the alternate hypothesis. H0: >72 ; H1: = 72 H0: = 72 ; H1: 72 H0: 72 ; H1: < 72 H0: 72 ; H1: > 72 b. State the decision rule. Reject H1 if z < 1.28 Reject H1 if z > 1.28 Reject H0 if z > 1.28 Reject H0 if z < 1.28 c. Compute the value of the test statistic. (Round your answer to 2 decimal places.) Value of the test statistic d. What is your decision regarding H0? Do not reject H0 Reject H0 e. What is the p-value? (Round your answer to 4 decimal places.) p-value The Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales representatives make an average of 40 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 38 sales representatives reveals that the mean number of calls made last week was 41. The standard deviation of the sample is 2.6 calls. Using the 0.025 significance level, can we conclude that the mean number of calls per salesperson per week is more than 40? H0 : 40 H1 : > 40 1. Compute the value of the test statistic. (Round your answer to 3 decimal places.) Value of the test statistic 2. What is your decision regarding H0? H0. The mean number of calls is (Click to select) than 40 per week. (Click to select) A United Nations report shows the mean family income for Mexican migrants to the United States is $27,150 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 30 Mexican family units reveals a mean to be $29,500 with a sample standard deviation of $11,150. Does this information disagree with the United Nations report? Apply the 0.01 significance level. a. State the null hypothesis and the alternate hypothesis. H0: = H1: b. State the decision rule for .01 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) Reject H0 if t is not between and c. Compute the value of the test statistic. (Round your answer to 2 decimal places.) Value of the test statistic d. Does this information disagree with the United Nations report? Apply the 0.01 significance level. . This data (Click to select) the report. (Click to select) The following information is available. H0 : 220 H1 : < 220 A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the .025 significance level. a. Is this a one- or two-tailed test? One-tailed test Two-tailed test b. What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) H0 when z < (Click to select) c. What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) Value of the test statistic d. What is your decision regarding H0? Reject Do not reject e. What is the p-value? (Round your answer to 4 decimal places.) p-value Given the following hypotheses: H0 : 10 H1 : > 10 A random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation 3. Using the .05 significance level: a. State the decision rule. (Round your answer to 3 decimal places.) Reject H0 if t > b. Compute the value of the test statistic. (Round your answer to 3 decimal places.) Value of the test statistic c. What is your decision regarding the null hypothesis? H0. There is (Click to select) evidence to conclude that the (Click to select) population mean is greater than 10. Given the following hypotheses: H0 : = 400 H1 : 400 A random sample of 12 observations is selected from a normal population. The sample mean was 407 and the sample standard deviation 6. Using the .01 significance level: a. State the decision rule. (Negative amount should be indicated by a minus sign. Round your answers to 3 decimal places.) Reject H0 when the test statistic is the interval ( (Click to select) b. Compute the value of the test statistic. (Round your answer to 3 decimal places.) , ). Value of the test statistic c. What is your decision regarding the null hypothesis? Do not reject A sample of 35 observations is selected from a normal population. The sample mean is 26, and the population standard deviation is 4. Conduct the following test of hypothesis using the 0.05 significance level. H0 : 25 H1 : > 25 a. Is this a one- or two-tailed test? "Two-tailed"-the alternate hypothesis is different from direction. "One-tailed"-the alternate hypothesis is greater than direction. b. What is the decision rule? (Round your answer to 3 decimal places.) H0, when z > (Click to select) c. What is the value of the test statistic? (Round your answer to 2 decimal places.) Value of the test statistic d. What is your decision regarding H0? Do not reject Reject There is evidence to conclude that the population mean is greater than 25. (Click to select) e. What is the p-value? (Round your answer to 4 decimal places.) p-value At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, \"You can average $72 a day in tips.\" Assume the population of daily tips is normally distributed with a standard deviation of $2.45. Over the first 34 days she was employed at the restaurant, the mean daily amount of her tips was $73.07. At the 0.10 significance level, can Ms. Brigden conclude that her daily tips average more than $72? a. State the null hypothesis and the alternate hypothesis. H0: >72 ; H1: = 72 H0: = 72 ; H1: 72 H0: 72 ; H1: < 72 H0: 72 ; H1: > 72 b. State the decision rule. Reject H1 if z < 1.28 Reject H1 if z > 1.28 Reject H0 if z > 1.28 Reject H0 if z < 1.28 c. Compute the value of the test statistic. (Round your answer to 2 decimal places.) Value of the test statistic d. What is your decision regarding H0? Do not reject H0 Reject H0 e. What is the p-value? (Round your answer to 4 decimal places.) p-value The Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales representatives make an average of 40 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 38 sales representatives reveals that the mean number of calls made last week was 41. The standard deviation of the sample is 2.6 calls. Using the 0.025 significance level, can we conclude that the mean number of calls per salesperson per week is more than 40? H0 : 40 H1 : > 40 1. Compute the value of the test statistic. (Round your answer to 3 decimal places.) Value of the test statistic 2. What is your decision regarding H0? H0. The mean number of calls is (Click to select) than 40 per week. (Click to select) A United Nations report shows the mean family income for Mexican migrants to the United States is $27,150 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 30 Mexican family units reveals a mean to be $29,500 with a sample standard deviation of $11,150. Does this information disagree with the United Nations report? Apply the 0.01 significance level. a. State the null hypothesis and the alternate hypothesis. H0: = H1: b. State the decision rule for .01 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) Reject H0 if t is not between and c. Compute the value of the test statistic. (Round your answer to 2 decimal places.) Value of the test statistic d. Does this information disagree with the United Nations report? Apply the 0.01 significance level. . This data (Click to select) the report. (Click to select) The following information is available. H0 : 220 H1 : < 220 A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the .025 significance level. a. Is this a one- or two-tailed test? One-tailed test Two-tailed test b. What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) H0 when z < (Click to select) c. What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) Value of the test statistic d. What is your decision regarding H0? Reject Do not reject e. What is the p-value? (Round your answer to 4 decimal places.) p-value Given the following hypotheses: H0 : 10 H1 : > 10 A random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation 3. Using the .05 significance level: a. State the decision rule. (Round your answer to 3 decimal places.) Reject H0 if t > b. Compute the value of the test statistic. (Round your answer to 3 decimal places.) Value of the test statistic c. What is your decision regarding the null hypothesis? H0. There is (Click to select) evidence to conclude that the (Click to select) population mean is greater than 10. Given the following hypotheses: H0 : = 400 H1 : 400 A random sample of 12 observations is selected from a normal population. The sample mean was 407 and the sample standard deviation 6. Using the .01 significance level: a. State the decision rule. (Negative amount should be indicated by a minus sign. Round your answers to 3 decimal places.) Reject H0 when the test statistic is the interval ( (Click to select) b. Compute the value of the test statistic. (Round your answer to 3 decimal places.) , ). Value of the test statistic c. What is your decision regarding the null hypothesis? Do not reject