Question

David wants to test a claim about a population mean. The population standard deviation is unknown, the sample is a simple random sample of size 20, and the population is normally distributed. In this case, the t-test should be used since σ is unknown. If David incorrectly uses the z-distribution instead of the t-distribution, will he obtain a P-value that is too big or too small? Explain your thinking. Will he be more likely or less likely to reject the null hypothesis than if had correctly used the t-distribution?

Answer 1

a)The P-value will be too small

b) He will reject the Null hypothesis

Explanation:

a) If David incorrectly uses the z-distribution instead of the t-distribution, he will obtain a p-value that is too small because p-values obtained using Z distribution are smaller when compared to p-values obtained using t-distribution

b) He will reject the Null hypothesis given that the P value he will obtain will be very different from the one he obtained using z-distribution