STAT 244 Exam

STAT 244 - Test: Take-Home FINAL

Name:

PART B: Take home. Each problem is worth 10 points.

INSTRUCTIONS: Please write out all work. In the case that the final answer is incorrect, as much partial credit as possible will be given. DUE FRIDAY 8/15

PROBLEM 1: A sample of 150 brand A blade emitters showed a mean lifetime of 1400 hours and a standard deviation of 125 hours. A sample of 175 brand B blade emitters showed a mean lifetime of 1200 hours and a standard deviation of 80 hours.

i. Find the 95% confidence interval for the difference of mean lifetime of the populations of brands A and B. ii. Find the 99% confidence interval for the difference of mean lifetime of the populations of brands A and B. iii. At 5% significance level is there sufficient evidence to warrant concluding a significant difference between the mean lifetimes of the populations of brands A and B? Using the confidence interval method, show the steps of your hypothesis test.

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PROBLEM 2: The mean lifetime of a sample of 100 hyperdrive motivators produced by a company is computer to be 1570 hours with a standard deviation of 120 hours. If µ is the mean lifetime of all hyperdrive motivators produced by the company, test the hypothesis µ = 1600 against the alternative H1 : µ 6= 1600.

i. Test the hypothesis at the 5% significance level. Use the critical value method. ii. Test the hypothesis at the 1% significance level. Use the critical value method. iii. Test the hypothesis µ = 1600 against the alternative µ < 1600 at the 1% significance level. Use the critical value method. iv. Was your result the same in part (ii) and (iii)? Why do you suppose that was?

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PROBLEM 3: An Jedi Knight has two classes of Younglings, A and B. Class A has 16 students while class B has 25 students. On the same examination, although there was not a significance difference in mean grades, class A had a standard deviation of 8 while class B had a standard deviation of 11.

i. At the 5% significance level can we conclude that the variability of class B is greater than that of class A? ii. What is the p−value of the test?

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PROBLEM 4: The table below shows the observed frequencies of Sebulba tossing a dueling die 120 times.

Face 1 2 3 4 5 6 Observed 25 23 17 16 14 24

i. Test the hypothesis that the die is a fair die, using the 5% level of significance. ii. Find the p−value of this test. iii. What is the lowest level of significance at which you can reject the null hypothesis?

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PROBLEM 5: The table below indicates the numbers of Younglings passed and failed by three instruc- tors: Obi-Wan Kenobi, Yoda, and Qui-Gon Jinn .

Frequencies Observed Kenobi Yoda Jinn TOTAL

Passed 50 47 56 153 Failed 5 14 8 27 TOTAL 55 61 64 180

i. Test the hypothesis that the proportions of the students failed by the three instructors are equal. Use 5% level of significance. ii. What is the p−value for this test?

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PROBLEM 6: A SRS of 32 bounties collected by Boba-Fett is shown below. (Assume all currency has been exchanged to the same currency.)

71 67 66 55 82 77 66 58 69 79 61 46 84 93 72 54 78 86 48 52 67 95 70 43 70 64 62 76 95 66 40 56

i. Using the sign test, test the hypothesis at the 5% level of significance that the median of the population of bounties Boba-Fett collects is 66. ii. What is the p−value for the test?

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PROBLEM 7: In 30 tosses of a Credcoin, the following sequence of heads (H) and tails (T) is obtained:

H T T H T H H H T H T H H T H H T H H T H T T H T H H T H T

i. Determine the number of runs, V. ii. Test at the 5% significance level whether the sequence is random.

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