Chapter 9, Problem 69PS

In hypothesis testing, the common level of significance is $\alpha =\mathrm{0.05.}$ Some might argue for a level of significance greater than 0.05. Suppose that web designers tested the proportion of potential web page visitors with a preference for a new web deign over the existing web design. The null hypothesis was that the population of web page visitors preferring the new design was 0.50, and alternative hypothesis was that it was not equal to 0.50. The P-value for the test was 0.20.

a. State, In statistical terms, the null and alternative hypotheses for this example.

b. Explain the risks associated with Type I and Type II error in this case.

c. What would be the consequence if you rejected the null hypothesis for a p-value of 0.20?

d. What might be an argument for raising the value of $\alpha ?$

e. What would you do in this situation?

f. What is you answer in (e) if the p-value equals 0.12? What if it equals 0.06?