Question

9. (1) If you reject the null hypothesis at n=64, then, for the same sample information, you would reject the null hypothesis if
n=25. T or F
10. (1) We can claim that if the p-value of a test is smaller than the probability of Type I error, then we would always reject the
null hypothesis. T or F
11. (1) The probability of Type I error and the probability of Type II error are inversely related. T or F
12. (1) Increasing the sample size will make both Type I and Type II errors fall. T or F
13. (1) A chain will open its stores if the mean income of the neighboring area is normal with a mean of $60,000 with a
standard deviation of $22,000. The probability that the average of 25 families is above $50,000 is more than the probability
of the average of 16 families being above $50,000. T or F
14. (1) If the probability of Type I error falls then the acceptance region increases in size. T or F
15. (1) If the acceptance region increases in size, then the probability of Type II Error will increase. T or F
16. (1) The p-value of the test gives you the likelihood of seeing the sample result if the null hypothesis was correct. T or F
17. (1) The smaller the p-value the more we disbelieve the null hypothesis. T or F
18. (1) If the confidence level of a problem falls, then so does α. T or F
19. (1) We can claim that all else equal, if the level of significance were smaller and the standard deviation was smaller, then we
would need a smaller sample to generate a confidence interval with the same margin of error. T or F

Answer 1

9. As the sample size decreases critical value increases. So chances for rejecting null hypothesis will also increased.

That is if we reject null hypothesis for n=64 then we will reject the null hypothesis for n=25 also.

Hence, it is true. Correct option is T.

10:

Yes if p-value is less than Type I error () we reject the null hypothesis.

Hence, it is true. Correct option is T.

11:

Yes, as the type I error increase, type II error decreases.

Correct option is T.

12:

Increases sample size decreases type II error but type I error remain same.

Correct option is F.

13:

For n=25 we have

So the probability that the average of 25 families is above $50,000 is

P(z > -2.27) = 0.9884

For n=16 we have

So the probability that the average of 16 families is above $50,000 is

P(z > -1.82) = 0.9656

Correct option is T.

14:

Correct option is T.

15:

Yes becuase type I error decreases. Which in turn will increase the type II error.

Correct option is T.

16:

Correct option is T.

17;

Correct option is T.

18:

Correct option is F.

19:

Correct option is F.