Assume a random sample, and sample mean of the sample as the test statistic. In

Question

Assume a random sample, and sample mean of the sample as the test statistic. In the context of a null hypothesis test, what effect does increasing the sample size have on:

a. the probability of committing a Type-I error tends to

A.increase

B.decrease

C.stay constant

D.not predictable

b. the probability of committing a Type-II error tends to

A.increase

B.decrease

C.stay constant

D.not predictable

c. the power of the test tends to

A.increase

B.decrease

C.stay constant

D.not predictable

d. the p-value of an identical observation tends to

A.increase

B.decrease

C.stay constant

D.not predictable

e. significance level tends to

A.increase

B.decrease

C.stay constant

D.not predictable

Explanation / Answer

a. Too large samples increase the type 1 error because the p-value depends on the size of the sample, but the alpha level of significance is fixed.

A.increase

b. Statistical power is positively correlated with thesample size, which means that given the level of theother factors, a larger sample size gives greater power. As we know Type II error is 1-power so value of Type II error will decrease

B.decrease

c. Statistical power is positively correlated with thesample size, which means that given the level of theother factors, a larger sample size gives greater power. As we know Type II error is 1-power so value of Type II error will decrease.

A.increase

d. Increasing the sample size will tend to result in a smaller P-value .

B.decrease

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