9.56 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 (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 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 is used?

9.58 Of 1,000 respondents aged 24 to 35, 65% reported that they preferred to “look for a job in a place where I would like to live” rather than “look for the best job I can find, the place where I live is secondary.” (Data extracted from L. Belkin, “What Do Young Jobseekers Want? (Something Other Than a Job),” The New York Times, September 6, 2007, p. G2.) At the 0.05 level of significance, is there evidence that the proportion of all young jobseekers aged 24 to 35 who preferred to “look for a job in a place where I would like to live” rather than “look for the best job I can find, the place where I live is secondary” is different from 60%?

9.59 The telephone company wants to investigate the desirability of beginning a marketing campaign that would offer customers the right to purchase an additional telephone line at a substantially reduced installation cost. The campaign will be initiated if there is evidence that more than 20% of the customers would consider purchasing an additional telephone line if it were made available at a substantially reduced installation cost. A random sample of 500 households is selected. The results indicate that 135 of the households would purchase the additional telephone line at a reduced installation cost.

a.   At the 0.05 level of significance, is there evidence that more than 20% of the customers would purchase the additional telephone line?

b.   How would the manager in charge of promotional programs concerning residential customers use the results in (a)?