An article in Marketing News (T. T. Semon, "Consider a Statistical Insignificance Test," Marketing News, February 1, 1999) argued that the level of significance used when comparing two products is often too low-that is, sometimes you should be using an value greater than 0.05. Specifically, the article recounted testing the proportion of potential customers with a preference for product 1 over product 2. The null hypothesis was that the population proportion of potential customers preferring product 1 was 0.50, and the alternative hypothesis was that it was not equal to 0.50. The p-value for the test was 0.22. The article suggested that, in some cases, this should be enough evidence to reject the null hypothesis.
a. State, in statistical terms, the null and alternative hypotheses for this example.
b. Explain the risks associated with Type I and Type II errors in this case.
c. What would be the consequences if you rejected the null hypothesis for a p-value of 0.22?
d. Why do you think the article suggested raising the value of ?
e. What would you do in this situation?
f. What is your answer in (e) if the p-value equals 0.12? What if it equals 0.06?