Question

1. If you see a p-value that is less than your cutoff, do you: (a) Reject the H0 (b) Reject the H1 (c) Fail to reject the H0 (d) Fail to reject the H1 (e) Accept the H0 (f) Accept the H1

6. Let X be a random variable with E(X) = 1, Var(X) = 4. I observe X¯ = 1.1 from a sample of size n. I am doing a hypothesis test of whether or not H0 : µ = 1 or H1 : µ 6= 1. As I increase n what will happen to the p-value? (a) It will increase (b) It will decrease (c) It will not change (d) Not enough information to conclude either way.

7. I am doing the same hypothesis test as above. As n increases, what will happen to the width of the confidence interval? (a) It will increase (b) It will decrease (c) It will not change (d) Not enough information to conclude either way.

8. I am testing to see if phones break faster than they're supposed to (they do). To test this, I set up two experiments. In the first one, I observed the mean time to break 200 iPhones, took the average of the breaking time, and then did a Z test on the average breaking time. In the second, for each of the 200 iPhones, I computed a Z statistic and got 200 p-values. In the first test, I got a p-value of 0.01. In the second test, the smallest of all the p-values I got was 0.04. If I apply Bonferroni correction with a threshold (α level) of 0.05, what is the correct set of conclusions to get from these tests: (a) Test 1 Reject null, Test 2 Reject All Null Hypotheses (b) Test 1 Reject null, Test 2 Do not Reject All Null Hypotheses (c) Test 1 Do not Reject null, Test 2 Reject All Null Hypotheses (d) Test 1 Do not Reject null, Test 2 Do not Reject All Null Hypotheses (e) Test 1 Reject null, Test 2 Not enough info (f) Test 2 Do not Reject null, Test 2 Not enough info

Answer 1

1. Amswer is (a) Reject the H0

Note : We reject the null hypothesis if P value < significaance level (which is the cutoff of the test)

6. Answer is (b) It will decrease

Note : Test statistic is

As n increases denominator of the test statistic decreases , which gives a higher value of test statistic zo

Now , P value = P( z > zo)

Thus as zo increases , P value decreases

7. Answer is (b) It will decrease

Note : The 95% (say) confidence interval is given by

where is the margin of error

As n increases margin of error decreases

Thus confidence interval becomes narrower

8. Answer is (b) Test 1 reject null , Test 2 donot reject all null hypotheses

Note : For test 2, P value = 0.01

Significance level ,

As P value < 0.05 : Reject the null hypothesis

For test 2, , Using Bonferroni correction ,for 200 tests significance level becomes

Lowest P value = 0.04 > 0.00025

That is all other P value > 0.00025

Fail to reject all null hypotheses