Carleton University
School of Mathematics and Statistics
STAT 2606 – Assignment #9 – Summer 2017
Due on Tuesday, August 1 before 3:00pm
INSTRUCTIONS:
I. Assignments are to be uploaded to the course website on cuLearn as a single legible PDF file by the
above due date and time. No late assignments will be accepted without sufficient advanced notice and a
legitimate, documented reason.
II. You must show and explain all of your work. No credit will be given for answers without justification.
III. This assignment is intended to represent your individual knowledge. It is not a group assignment.
Sudoku puzzles all night. He claims that, on average, it takes him 6 minutes to complete a medium difficulty puzzle. To test his claim, he randomly selected 36 puzzles of medium difficulty and found that, on average, it took him 6.7 minutes to complete each puzzle. Assuming that the population standard deviation of completion times is 3.8 minutes, is there sufficient evidence to suggest that, on average, it actually takes Wayne more than 6 minutes to complete each puzzle? Using the p-value method, conduct an appropriate hypothesis test at ? = 0.05. Comment on the validity of the result.
the claim that the average time it takes her and her staff to complete a haircut is less than 15 minutes. A
random sample of eight haircuts yielded the following service times, measured to the nearest minute:
8 9 10 11 12 12 13 16 At the 10% level of significance, does this sample provide evidence to support Barbara’s claim? Conduct an
appropriate hypothesis test using the p-value method, and comment on the validity of the result.
3. For the situation described in each part, give the p-value, or a range for the p-value, associated with the
hypothesis test. For the purposes of this question, you may assume that each sample is randomly drawn from
a normally distributed population. HINT: In each case, you must decide if you would use a z-test or t-test.
(a) Ha: µ ? µ 0 , n = 12, ? unknown, test statistic = 2.54
(b) Ha: µ ? µ 0 , n = 15, ? known, test statistic = –1.87
(c) Ha: µ > µ 0 , n = 24, ? unknown, test statistic = 4.21
(d) Ha: µ > µ 0 , n = 120, ? unknown, test statistic = 1.34
(e) Ha: µ < µ 0 , n = 8, ? unknown, test statistic = –2.76
(f) Ha: µ < µ 0 , n = 14, ? unknown, test statistic = –1.21 © 2017 Wayne Horn
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