Question

The time taken for healthy Canadian adults to complete a logic problem is believed to have a mean 40 seconds. It is of interest to investigate whether UBC students perform better on average than healthy adult Canadians, so the logic problem is given to a sample of 80 UBC students, and their times to solution are recorded. The sample mean and standard deviation are 36 seconds and 17 seconds.

Part a) What is/are the parameters of interest relevant to this hypothesis test? Choose all parameters that you use to set up the null and alternative hypotheses, as well as those referenced in the assumptions and derivation of the relevant test statistic.
A. 40 seconds
B. The mean time for all UBC students to complete the logic problem.
C. The mean time for the 80 UBC students to complete the logic problem.
D. 80
E. None of the above

Part B) In testing a hypothesis about a parameter of interest, what would your null hypothesis be?
A. The mean time taken to solve the logic problem by healthy Canadian adults is 40 seconds.
B. The mean time taken to solve the logic problem by healthy Canadian adults is greater than 40 seconds.
C. The mean time taken to solve the logic problem by healthy Canadian adults is less than 40 seconds.
D. The mean time taken to solve the logic problem by healthy Canadian adults is different from 40 seconds.
E. The mean time taken to solve the logic problem by UBC students is greater than 40 seconds.
F. The mean time taken to solve the logic problem by UBC students is less than 40 seconds.
G. The mean time taken to solve the logic problem by UBC students is different from 40 seconds.
H. The mean time taken to solve the logic problem by UBC students is 40 seconds.

Part c) You would take the alternative hypothesis to be:
A.one-sided, left-tailed
B. two-sided.
C. one-sided, right-tailed.
D. it does not matter whether we take a one-sided or two-sided alternative.

Part d) Compute the test statistic (Please round your answer to three decimal places:

Part e) Assume all necessary conditions are met (random sampling, independence samples, large enough sample size). Which of the following approximate the sampling distribution of the test statistic in Part d:
A. Normal distribution
B. t-distribution

Part f) Suppose that, based on data collected, you reject the null hypothesis. Which of the following could you conclude?
A.There is sufficient evidence to suggest the mean time taken to solve the logic problem by UBC students is less than the mean time for healthy adult Canadians.
B.There is sufficient evidence to suggest the mean time taken to solve the logic problem by UBC students is the same as the mean time for healthy adult Canadians.
C. There is sufficient evidence to suggest the mean time taken to solve the logic problem by UBC students is greater than the mean time for healthy adult Canadians.
D.There is insufficient evidence to suggest the mean time taken to solve the logic problem by UBC students is the same as the mean time for healthy adult Canadians.
E. There is insufficient evidence to suggest the mean time taken to solve the logic problem by UBC students is less than the mean time for healthy adult Canadians.

Part g) Suppose that, based on data collected, you decide that UBC students perform better on average than healthy adult Canadians.
A. it is possible that you are making a Type I error.
B. it is possible that you are making a Type II error.
C. it is certainly correct that UBC students perform better on average than healthy adult Canadians.
D. it is certainly incorrect that UBC students perform better on average than healthy adult Canadians.
E. there must have been a problem with the way the sample was obtained.

Part h) Suppose that, based on the data collected, you obtain a PP-value of 0.02 (confirm this using the t-table). This means:

A. there is a 2% chance that UBC students perform better on average than healthy adult Canadians.
B. there is a 2% chance that UBC students perform worse on average than healthy adult Canadians.
C. the probability of UBC students performing as well or better is 0.02, if indeed the true mean time taken to solve the logic problem by all UBC students is 40 seconds.
D. the probability of UBC students performing as well or worse is 0.02, if indeed the true mean time taken to solve the logic problem by all UBC students is 40 seconds.
E. the sample of UBC students performed relatively worse, if indeed the true mean time taken to solve the logic problem by all UBC students is 40 seconds.

F. the sample of UBC students performed relatively better, if indeed the true mean time taken to solve the logic problem by all UBC students is 40 seconds.

Answer 1

part a)

A. 40 seconds

C. The mean time for the 80 UBC students to complete the logic problem.

part B)

H. The mean time taken to solve the logic problem by UBC students is 40 seconds.

Part c)

A.one-sided, left-tailed

part d) test statistic is given by

(36-40)*/17 = -2.104

part e) A. Normal distribution

part f) A.There is sufficient evidence to suggest the mean time taken to solve the logic problem by UBC students is less than the mean time for healthy adult Canadians.

part g) B. it is possible that you are making a Type II error.

part h) F. the sample of UBC students performed relatively better, if indeed the true mean time taken to solve the logic problem by all UBC students is 40 seconds.