Question

We have a one sample test for the population mean. The significance level is a fixed value. Suppose we increase the sample size. Assume the true mean equals the null mean.

(a) The t critical value moves closer to zero.

(b) The size of the rejection region decreases

(c) The probability of a Type I error decreases

(d) The probability of a Type I error increases

Answer 1

Solution:

Correct option is

(d) The probability of a Type I error increases

Explanation:

For one sample test for the population mean

Test statistic z =

Observe that as sample size increases , magnitude of the test statistic value increases.

Then the probability of rejecting the null hypothesis increases.

We know , Type I error is "rejecting the null hypothesis , when in fact the null hypothesis is true "

So , as the sample size n increases , the

The probability of a Type I error increases