The time taken for healthy Canadian adults to complete a logic problem is believ

Question

The time taken for healthy Canadian adults to complete a logic problem is believed to be Normally distributed with mean 40 seconds and standard deviation 4 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.

Part a) What is the parameter of interest relevant to testing the hypothesis mentioned above?
A. The mean time for all UBC students to complete the logic problem.
B. The mean time for the 80 UBC students to complete the logic problem.
C. 80
D. None of the above

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

Part c) For testing the hypothesis about the parameter of interest identified in (a), your alternative hypothesis would be:
A. it does not matter whether we take a one-sided or two-sided alternative.
B. one-sided, left-tailed.
C. one-sided, right-tailed.
D. two-sided.

Part d) Suppose that, based on data collected, you reject the null hypothesis. Which of the following could you conclude?
A. 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.
B. There is insufficient 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.
C. 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.
D. 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.
E. 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.
F. 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.

Part e) 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. there must have been a problem with the way the sample was obtained.
D. it is certainly correct that UBC students perform better on average than healthy adult Canadians.
E. it is certainly incorrect that UBC students perform better on average than healthy adult Canadians.

Part f) Suppose that, based on the data collected, you obtain a PP-value of 0.04. This means:
A. the probability of UBC students performing as well or worse is 0.04, if indeed the true mean time taken to solve the logic problem by all UBC students is 40 seconds.
B. there is a 4% chance that UBC students perform better on average than healthy adult Canadians.
C. the probability of UBC students performing as well or better is 0.04, if indeed the true mean time taken to solve the logic problem by all UBC students is 40 seconds.
D. 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.
E. there is a 4% chance that UBC students perform worse on average than healthy adult Canadians.
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.

Part g) Based on the PP-value that was obtained, you would (Select all that apply):
A. reject the null hypothesis at =0.1=0.1 level of significance
B. reject the null hypothesis at =0.05=0.05 level of significance
C. fail to reject the null hypothesis at all.
D. neither reject nor accept the null hypothesis.
E. believe the null hypothesis is true.
F. None of the above.

Explanation / Answer

Part a)

A. The mean time for all UBC students to complete the logic problem.

Part b)

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

Part c)

B. one-sided, left-tailed.

Part d)

C. 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 e)

A. it is possible that you are making a Type I error.

Becuase type I error is probabaility of rejecting true null hypothesis.

Part f)

E. there is a 4% chance that UBC students perform worse on average than healthy adult Canadians.

Part g)

A. reject the null hypothesis at =0.1 level of significance
B. reject the null hypothesis at =0.05=0.05 level of significance

Becuase p-value is less than =0.1 so we reject the null hypothesis at =0.1 level of significance.

Becuase p-value is less than =0.05 so we reject the null hypothesis at =0.05 level of significance.

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