Testing a Claim about a Difference between Means Answers

Can a person train to become better at holding their breath? An experiment was designed to find out. Twelve volunteers were randomly assigned to 1 of 2 groups. The 6 volunteers assigned to group 1 were given breath-holding exercises to perform for 2 weeks. The other group was not given any information about the experiment. At the end of the 2 weeks, all 12 volunteers were individually tested to determine how long they could hold their breath. Here are the data (in seconds).Group 1: 90, 88, 70, 110, 75, 105Group 2: 40, 48, 35, 50, 55, 62

A manufacturing company packages shipments in either large or small boxes. A random sample of 40 shipments that are packaged in large boxes is found to have a mean of 15 pounds and a standard deviation of 2.8 pounds. A separate random sample of 50 shipments that are packaged in small boxes is found to have a mean of 10 pounds and a standard deviation of 1.5 pounds. The manager would like to know if the data provide convincing evidence that the true mean weight of all shipments that are packaged in small boxes is less than the true mean weight of all shipments that are packaged in large boxes. The manager tests H0: μS – μL = 0, Ha: μS – μL < 0, where μL = the true mean weight of all shipments that are packaged in large boxes and μS = the true mean weight of all shipments that are packaged in small boxes. The conditions for inference have been met. What are the values of the test statistic and P-value for a t-test about a difference in means?Find the t-table here and the z-table here.

A student claims that professional male basketball players are taller, on average, than college male basketball players. To investigate this claim, the student selects a random sample of 30 professional basketball players and 30 college basketball players. The mean height of the sample of professional male basketball players is 76 inches with a standard deviation of 3.5 inches. The mean height of the sample of college male basketball players is 74.5 inches with a standard deviation of 5.5 inches. The student would like to determine if there is convincing evidence that the true mean height of all professional male basketball players is greater than the true mean height of all college male basketball players. The hypotheses H0: μ1 – μ2 = 0, Ha: μ1 – μ2 > 0 are tested where μ1 = the true mean height of all professional male basketball players, and μ2 = the true mean height of all college male basketball players. The conditions for inference have been met. What are the values of the test statistic and P-value for a t-test about a difference in means?Find the t-table here and the z-table here.

A manufacturing company packages shipments in either large or small boxes. A random sample of 40 shipments that are packaged in large boxes is found to have a mean of 15 pounds and a standard deviation of 2.8 pounds. A separate random sample of 50 shipments that are packaged in small boxes is found to have a mean of 10 pounds and a standard deviation of 1.5 pounds. The manager would like to know if the data provide convincing evidence that the true mean weight of all shipments that are packaged in small boxes is less than the true mean weight of all shipments that are packaged in large boxes. The manager tests H0: μS – μL = 0, Ha: μS – μL < 0, where μL = the true mean weight of all shipments that are packaged in large boxes and μS = the true mean weight of all shipments that are packaged in small boxes. The conditions for inference have been met. The standardized test statistic is t = –10.19 and the P-value is less than 0.0005. What conclusion should be made using the significance level = 0.01?

A student claims that professional male basketball players are taller, on average, than college male basketball players. To investigate this claim, the student selects a random sample of 30 professional basketball players and 30 college basketball players. The mean height of the sample of professional male basketball players is 76 inches with a standard deviation of 3.5 inches. The mean height of the sample of college male basketball players is 74.5 inches with a standard deviation of 5.5 inches. The student would like to determine if there is convincing evidence that the true mean height of all professional male basketball players is greater than the true mean height of all college male basketball players. Let μ1 = the true mean height of all professional male basketball players and μ2 = the true mean height of all college male basketball players. Are the conditions for inference met?

Timmy could follow two main routes to get to school. Timmy believes that route 1 is faster than route 2. To investigate, he decides to keep track for the next 4 weeks. Each morning, he flips a coin to determine which route he takes. Of the 20 school days, 12 days were randomly assigned to route 1, and 8 days were randomly assigned to route 2. The mean travel time for days assigned to route 1 was 20 minutes with a standard deviation of 3 minutes. The mean travel time for the days assigned to route 2 was 22 minutes with a standard deviation of 2 minutes. Timmy would like to know if the data provide convincing evidence of a difference in travel time for the 2 routes. Let μ1 = the true mean travel time to school along route 1 and μ2 = the true mean travel time to school along route 2. Dotplots of the distribution of travel time for route 1 and route 2 show no strong skewness or outliers. Are the conditions for inference met?

Jocelyn believes that the amount of sleep she tends to get on weekends differs from the amount of sleep she tends to get during the school week. To investigate this claim, she randomly selects 10 weekend days and 10 school days. She consults her smart watch to determine the number of hours she slept for each of the selected days. Here are the data.School week: 7, 7.5, 8, 6.5, 8, 7.5, 7, 6.5, 7, 8Weekend: 9.5, 9.5, 8.25, 8.5, 7.5, 10.25, 8, 7, 9.5, 10

Timmy could follow two main routes to get to school. Timmy believes that route 1 is faster than route 2. To investigate, he decides to keep track for the next 4 weeks. Each morning, he flips a coin to determine which route he takes. Of the 20 school days, 12 days were randomly assigned to route 1, and 8 days were randomly assigned to route 2. The mean travel time for days assigned to route 1 was 20 minutes with a standard deviation of 3 minutes. The mean travel time for the days assigned to route 2 was 22 minutes with a standard deviation of 2 minutes. Timmy would like to know if the data provide convincing evidence of a difference in travel time for the 2 routes, so he tests H0: μ1 – μ2 = 0, Ha: μ1 – μ2 ≠ 0. Let μ1 = the true mean travel time to school along route 1 and μ2 = the true mean travel time to school along route 2. Dotplots of the distribution of travel time for route 1 and route 2 show no strong skewness or outliers. The conditions for inference have been met. The standardized test statistic is t = –1.79, and the P-value is between 0.05 and 0.10. What conclusion should be made using the significance level, = 0.05?

A student claims that professional male basketball players are taller, on average, than college male basketball players. To investigate this claim, the student selects a random sample of 30 professional basketball players and 30 college basketball players. The mean height of the sample of professional male basketball players is 76 inches with a standard deviation of 3.5 inches. The mean height of the sample of college male basketball players is 74.5 inches with a standard deviation of 5.5 inches. The student would like to determine if there is convincing evidence that the true mean height of all professional male basketball players is greater than the true mean height of all college male basketball players.

A student claims that professional male basketball players are taller, on average, than college male basketball players. To investigate this claim, the student selects a random sample of 30 professional basketball players and 30 college basketball players. The mean height of the sample of professional male basketball players is 76 inches with a standard deviation of 3.5 inches. The mean height of the sample of college male basketball players is 74.5 inches with a standard deviation of 5.5 inches. The student would like to determine if there is convincing evidence that the true mean height of all professional male basketball players is greater than the true mean height of all college male basketball players. The hypotheses H0: μ1 – μ2 = 0, Ha: μ1 – μ2 > 0are tested, where μ1 = the true mean height of all professional male basketball players and μ2 = the true mean height of all college male basketball players. The conditions for inference have been met. The standardized test statistic is t = 1.26, and the P-value is between 0.10 and 0.15. What conclusion should be made using the significance level, = 0.05?