AnswersStatisticsTesting a Claim about a Difference between Means

Testing a Claim about a Difference between Means — Quiz Answers

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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 point 5 inches. The mean height of the sample of college male basketball players is 74 point 5 inches with a standard deviation of 5 point 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 ratio of cap h sub 0 to mu sub 1 minus mu sub 2 is equal to 0 , ratio of cap h sub A to mu sub 1 minus mu sub 2 is greater than 0 are tested, where mu sub 1 is equal to the true mean height of all professional male basketball players and mu sub 2 is equal to the true mean height of all college male basketball players. The conditions for inference have been met. The standardized test statistic is t is equal to 1 point 2 6 , and the cap p -value is between 0 point 1 0 and 0 point 1 5 What conclusion should be made using the significance level, alpha is equal to 0 point 0 5 ?

A
Reject cap h sub 0 . 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.
B
Reject cap h sub 0 . There is not 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.
C
Fail to reject cap h sub 0 . There is not 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.
D
Fail to reject cap h sub 0 . 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.
3

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 point 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 point 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 ratio of cap h sub 0 to mu sub cap s minus mu sub cap l is equal to 0 , ratio of cap h sub A to mu sub cap s minus mu sub cap l is less than 0 , where mu sub cap l is equal to the true mean weight of all shipments that are packaged in large boxes and mu sub cap s is equal to 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 is equal to negative 10 point 1 9 and the cap p -value is less than 0 point 0 0 0 5 What conclusion should be made using the significance level alpha is equal to 0 point 0 1 ?

A
Fail to reject cap h sub 0 . There is convincing evidence that the true mean weight of all shipments packaged in small boxes is less than the true mean weight of all shipments packaged in large boxes.
B
Fail to reject cap h sub 0 . There is not convincing evidence that the true mean weight of all shipments packaged in small boxes is less than the true mean weight of all shipments packaged in large boxes.
C
Reject cap h sub 0 . There is not convincing evidence that the true mean weight of all shipments packaged in small boxes is less than the true mean weight of all shipments packaged in large boxes.
D
Reject cap h sub 0 . There is convincing evidence that the true mean weight of all shipments packaged in small boxes is less than the true mean weight of all shipments packaged in large boxes.
5

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 point 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 point 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. Let mu sub cap l is equal to the true mean weight of all shipments that are packaged in large boxes and mu sub cap s is equal to the true mean weight of all shipments that are packaged in small boxes. What are the appropriate hypotheses?

A
ratio of cap h sub 0 to mu sub cap s minus mu sub cap l is equal to 0 , ratio of cap h sub A to mu sub cap s minus mu sub cap l is less than 0
B
ratio of cap h sub 0 to mu sub cap s minus mu sub cap l is less than 0 , ratio of cap h sub A to mu sub cap s minus mu sub cap l is equal to 0
C
ratio of cap h sub 0 to mu sub cap s minus mu sub cap l is equal to 0 , ratio of cap h sub A to mu sub cap s minus mu sub cap l is greater than 0
D
ratio of cap h sub 0 to mu sub cap s minus mu sub cap l is greater than 0 , ratio of cap h sub A to mu sub cap s minus mu sub cap l is equal to 0
6

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 ratio of cap h sub 0 to mu sub 1 minus mu sub 2 is equal to 0 , ratio of cap h sub A to mu sub 1 minus mu sub 2 is not equal to 0 Let mu sub 1 is equal to the true mean travel time to school along route 1 and mu sub 2 is equal to 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. What are the values of the test statistic and cap p -value for a t - test about a difference in means? Use the t -table.

A
t is equal to negative 1 point 7 9 . The cap p -value is between 0 point 0 2 5 and 0 point 0 5 .
B
t is equal to negative 1 point 7 9 . The cap p -value is between 0 point 0 5 and 0 point 1 0 .
C
t is equal to 1 point 7 9 . The cap p -value is between 0 point 0 2 5 and 0 point 0 5 .
D
t is equal to 1 point 7 9 . The cap p -value is between 0 point 0 5 and 0 point 1 0 .
9

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 point 5 inches. The mean height of the sample of college male basketball players is 74 point 5 inches with a standard deviation of 5 point 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 ratio of cap h sub 0 to mu sub 1 minus mu sub 2 is equal to 0 , ratio of cap h sub A to mu sub 1 minus mu sub 2 is greater than 0 are tested where mu sub 1 is equal to the true mean height of all professional male basketball players, and mu sub 1 is equal to 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 cap p -value for a t -test about a difference in means? Use the t -table and the z -table.

A
z is equal to negative 1 point 2 6 . The cap p -value is 0 point 1 0 3 8 .
B
z is equal to 1 point 2 6 . The cap p -value is 0 point 1 0 3 8 .
C
t is equal to negative 1 point 2 6 . The cap p -value is between 0 point 1 0 and 0 point 1 5 .
D
t is equal to 1 point 2 6 . The cap p -value is between 0 point 1 0 and 0 point 1 5 .

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