• HealthLife spent $3 million to promote awareness and a positive image of its wellness services among Fortune 500 companies and their employees. They estimate a total target audience of around 10,000. To assess the campaign, the company conducted a pretest and a posttest. 
• Unaided awareness (“What companies come to mind when you think of companies that provide group health care coverage?”) increased from 21 percent in the pretest to 25 percent in the posttest. The values for positive perceptions of the brand image test were 42 percent and 44 percent. 
• However, the size of the random samples was only 100 for the tests. At 95 percent, sampling error for the awareness and image measures were ±8.7 and ±9.9 percent respectively (using posttest percents). 
• Based on the relatively small changes in awareness and positive image and the relatively large errors associated with these measures, HealthLife could not conclude with any confidence that either measure had changed. The CEO of HealthLife wants a more sensitive test regarding the effect of the advertising.

1. Show how the sampling error calculations for the posttest measures were calculated.

2. If the CEO wanted to be sure that the estimates of awareness and positive image are within ±2 percent of the true value at 95 percent confidence, what is the required sample size?

3. Using all the same information used in question 2, what is the required sample size if the CEO wants to be 99.5 percent confident?

4. If the current budget for conducting the telephone interviews is $20,000 and the cost per interview is $19, can HealthLife reach the goal specified in question 3? What error levels can it reach for both measures with the $20,000 budget? What is the required budget to reach the goal set in question 3?