If other factors are held constant, what is the effect of increasing the sample

Question

If other factors are held constant, what is the effect of increasing the sample size? (Hint: Look at the formulas for the estimated standard error and t-test for a single sample to figure out the answer).

A. It will increase the estimated standard error and increase the likelihood of rejecting H0. B. It will decrease the estimated standard error and decrease the likelihood of rejecting H0. C. It will decrease the estimated standard error and increase the likelihood of rejecting H0. D. It will increase the estimated standard error and decrease the likelihood of rejecting H0.

Explanation / Answer

here as std error is inversely proportional to square root of sample size; therefore it will decreases with increases of sample size.

hence

C. It will decrease the estimated standard error and increase the likelihood of rejecting H0.

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