When testing a claim about a population mean with a sample random sample selecte

Question

When testing a claim about a population mean with a sample random sample selected from a normally distributed population with unknown , the Student t-distribution should be used for finding the critical values and / or p-values. If the standard normal distribution is incorrectly used with the estimate s of , does that mistake make you more or less likely to reject the null hypothesis, or does it not make a difference? Explain. (Hint: How does the length of the 95% t confidence interval compare with that of the 95% z confidence interval? What does that mean about the cutoff value for rejection of a null hypothesis when using the t-distribution versus using the normal distribution?)

Explanation / Answer

As t-distribution has fatter tails than normal distribution, so the critical t-values are larger than the z-critical value at same level of significance., so if we use standard normal distribution incorrectly then we are more likely to reject the null hypothesis because critical values will be lower as compared to t-critical value.

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