You are testing a claim and incorrectly use the normal sampl

You are testing a claim and incorrectly use the normal sampling distribution instead of the t-sampling distribution. Does this make it more or less likely to reject the null hypothesis? Is this result the same no matter whether the test is left-tailed, right-tailed, or two-tailed?

Solution

yes. When the sample size is small, curve of t-sitribution is more fatter than curve of normal distribution. So for same level of significnace t-distrbution has more area under the tails in comparison to normal distribution. So chances for rejecting null hypothesis increases. For example: The z-score has critical values +1.96 for 5% level of significance. In contrast, for the t-distribution for a sample size of 15, 3.7% area is above +1.96 and 3.7% area is below -1.96 .

It is does not matter whether the test is left-tailed, right-tailed, or two-tailed.

However, when sample sizes are bigger than 30, the differences in critical values between the t-distribution and the normal-shaped sampling distribution are not significant.