1. In a survey of 500 individuals, it was found that 155 of the 500 rented at least one video from a video rental store during the past week. Test the hypothesis that 25% of the population rented at...

1. In a survey of 500 individuals, it was found that 155 of the 500 rented at least one video from a video rental store during the past week. Test the hypothesis that 25% of the population rented at least one video during the past week using a two-tailed alternative and α = 0.05. Perform the test using both the standard normal distribution and the chi-square distribution. Show that the chi-square test involving only two categories is equivalent to the significance test for proportions given in Chapter 10.

2. (a) Prove that formula (1) of this chapter can be written

(b) Use the result of part (a) to verify the value of x² computed in Problem 12.6.