Online magazines make it easy for readers to link to an advertiser's website directly from an advertisement placed in the digital magazine. A recent survey indicated that 56% of online magazine readers have clicked on an advertisement and linked directly to the advertiser's website. The survey was based on a sample size of n = 6,403. (Data extracted from "Metrics," EContent, January/February, 2007, p. 20.)
a. Use the five-step p-value approach to try to determine whether there is evidence that more than half of all the readers of online magazines have linked to an advertiser's website. (Use the 0.05 level of significance.)
b. Suppose that the sample size was only n = 100, and, as before, 56% of the online magazine readers indicated that they had clicked on an advertisement to link directly to the advertiser's website. Use the five-step p-value approach to try to determine whether there is evidence that more than half of all the readers of online magazines have linked to an advertiser's website. (Use the 0.05 level of significance.)
c. Discuss the effect that sample size has on hypothesis testing.
d. What do you think are your chances of rejecting any null hypothesis concerning a population proportion if a sample size of n = 20 is used?