Preparing to Test a Claim about a Mean Answers

A company that makes robotic vacuums claims their newest model of vacuum lasts, on average, two hours when starting on a full charge. To investigate this claim, a consumer group purchases a random sample of five vacuums of this model. They charge each unit fully and then measure the amount of time each unit runs. Here are the data (in hours): 2.2, 1.85, 2.15, 1.95, and 1.90. They would like to know if the data provide convincing evidence that the true mean run time differs from two hours. What are the appropriate hypotheses?

A company that makes robotic vacuums claims that their newest model of vacuum lasts, on average, two hours when starting on a full charge. To investigate this claim, a consumer group purchases a random sample of five vacuums of this model. They charge each unit fully and then measure the amount of time each unit runs. Here are the data (in hours): 2.2, 1.85, 2.15, 1.95, and 1.90. They would like to know if the data provide convincing evidence that the true mean run time differs from two hours. The consumer group plans to test the hypotheses H0: μ = 2 versus Ha: μ ≠ 2, where μ = the true mean run time for all vacuums of this model. The conditions for inference are met. The test statistic is t = 0.14 and the P-value is greater than 0.25. What conclusion should be made at the significance level, ?

A student claims that statistics students at her school spend, on average, an hour doing statistics homework each night. In an attempt to substantiate this claim, she selects a random sample of 6 of the 62 students who are taking statistics currently and asks them how much time they spend completing statistics homework each night. Here are the data (in hours): 0.75, 0.75, 0.75, 0.5, 1, 1.25. She would like to know if the data provide convincing statistical evidence that the true mean amount of time that statistics students spend doing statistics homework each night is less than one hour. The student plans to test the hypotheses, H0: μ = 1 versus Ha: μ < 1, where μ = the true mean amount of time that statistics students spend doing statistics homework each night. The conditions for inference are met. The test statistic is t = –1.58 and the P-value is between 0.05 and 0.10. What conclusion should be made at the significance level, ?

A pool supply company sells 50-pound buckets of chlorine tablets. A customer believes that the company may be underfilling the buckets. To investigate, an inspector is hired. The inspector randomly selects 30 of these buckets of chlorine tablets and weighs the contents of each bucket. The sample mean is 49.4 pounds with a standard deviation of 1.2 pounds. The inspector would like to know if this provides convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds, so he plans to test the hypotheses H0: μ = 50 versus Ha: μ < 50, where μ = the true mean weight of all 50-pound buckets of chlorine tablets. Are the conditions for inference met?

A student claims that statistics students at her school spend, on average, an hour doing statistics homework each night. In an attempt to substantiate this claim, she selects a random sample of 6 of the 62 students that are taking statistics currently and asks them how much time they spend completing statistics homework each night. Here are the data (in hours): 0.75, 0.75, 0.75, 0.5, 1, 1.25. She would like to know if the data provide convincing statistical evidence that the true mean amount of time that statistics students spend doing statistics homework each night is less than one hour. The student plans to test the hypotheses, H0: μ = 1 versus Ha: μ < 1, where μ = the true mean amount of time that statistics students spend doing statistics homework each night. The conditions for inference are met. What are the appropriate test statistic and P-value?Find the t-table here.

A student claims that statistics students at her school spend, on average, an hour doing statistics homework each night. In an attempt to substantiate this claim, she selects a random sample of 6 of the 62 students who are taking statistics currently and asks them how much time they spend completing statistics homework each night. Here are the data (in hours): 0.75, 0.75, 0.75, 0.5, 1, 1.25. She would like to know if the data provide convincing statistical evidence that the true mean amount of time that statistics students spend doing statistics homework each night is less than one hour. What are the appropriate hypotheses?

An engineer would like to design a parking garage in the most cost-effective manner. He reads that the average height of pickup trucks, which is the largest type of vehicle that should be expected to fit into the parking garage is 76.4 inches. To double-check this figure, the engineer employs a statistician. The statistician selects a random sample of 100 trucks and finds the mean height of the sample to be 77.1 inches with a standard deviation of 5.2 inches. The statistician will determine if these data provide convincing evidence that the true mean height of all trucks is greater than 76.4 inches. The statistician plans to test the hypotheses, H0: μ = 76.4 versus Ha: μ > 76.4, where μ = the true mean height of all trucks. The conditions for inference are met. What are the appropriate test statistic and P-value?Find the t-table here and the z-table here.

A company that makes robotic vacuums claims that their newest model of vacuum lasts, on average, two hours when starting on a full charge. To investigate this claim, a consumer group purchases a random sample of five vacuums of this model. They charge each unit fully and then measure the amount of time each unit runs. Here are the data (in hours): 2.2, 1.85, 2.15, 1.95, and 1.90. They would like to know if the data provide convincing evidence that the true mean run time differs from two hours. The consumer group plans to test the hypotheses H0: μ = 2 versus Ha: μ ≠ 2, where μ = the true mean run time for all vacuums of this model. The conditions for inference are met. What are the appropriate test statistic and P-value?Find the t-table here.

An engineer would like to design a parking garage in the most cost-effective manner. He reads that the average height of pickup trucks, which is the largest type of vehicle that should be expected to fit into the parking garage, is 76.4 inches. To double-check this figure, the engineer employs a statistician. The statistician selects a random sample of 100 trucks and finds the mean height of the sample to be 77.1 inches with a standard deviation of 5.2 inches. The statistician will determine if these data provide convincing evidence that the true mean height of all trucks is greater than 76.4 inches. The statistician plans to test the hypotheses, H0: μ = 76.4 versus Ha: μ > 76.4, where μ = the true mean height of all trucks. Are the conditions for inference met?

An engineer would like to design a parking garage in the most cost-effective manner. He reads that the average height of pickup trucks, which is the largest type of vehicle that should be expected to fit into the parking garage, is 76.4 inches. To double-check this figure, the engineer employs a statistician. The statistician selects a random sample of 100 trucks and finds the mean height of the sample to be 77.1 inches with a standard deviation of 5.2 inches. The statistician will determine if these data provide convincing evidence that the true mean height of all trucks is greater than 76.4 inches. What are the appropriate hypotheses?