Question 6.69

6.69 What’s wrong?

Here are several situations in which there is an incorrect application of the ideas presented in this section. Write a short explanation of what is wrong in each situation and why it is wrong.

  1. The statistic had a value of for a two-sided test. The null hypothesis is not rejected for because .
  2. A two-sided test is conducted to test , and the observed sample mean is . The null hypothesis is rejected because .
  3. The statistic had a value of 1.2 for a two-sided test. The -value was calculated as .
  4. The observed sample mean is 5 for a sample size . The population standard deviation is 2. For testing the null hypothesis mean of , a statistic of is calculated.

6.69

(a) For , we reject when is either bigger than 1.96 or smaller than . (b) You cannot just compare to ; we need to do a hypothesis test. (c) The -value is always the tail probability, so it should be . (d) is missing from the formula.