Show how the sampling error calculations for the posttest

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Reference no: EM131800718

Health Life is a leading provider of employee wellness programs to Fortune 500 companies. Its programs are designed to improve employee health and wellness with the goal of developing a healthier, happier, more productive workforce. In addition, it has shown that its programs reduce medical claims for its clients. This is an important consideration given that nearly all of its clients are self-insured in regard to medical benefits.

The company offers an array of programs and can tailor programs to the needs of individual clients. Health Life is about to start the second year of a brand image campaign. The company is planning to spend $3.5 million to promote awareness and a positive image of its services among Fortune 500 companies and their employees.

It is pursuing this strategy because the market for its services is becoming more competitive as interest in employee wellness has grown and as more competitors have entered the market in recent years. In the first year of the brand image campaign, Health Life spent $3 million pursuing the same goals of increasing awareness and building its image. In order to see if the campaign was successful, the company conducted tracking research by telephone. It conducted a pretest before the campaign began and a posttest on its conclusion.

The surveys were designed to measure awareness of Health Life and the image of Health Life among decision makers in Fortune 500 companies. Health life estimates an average of 20 executives were involved in the decision-making process for the purchase of its services per company, or a total target audience of around 10,000. Changes in either measure from the pretest to the posttest were to be attributed to the effects of the ad campaign. No other elements of this marketing strategy were changed during the course of the campaign.

Unaided or top-of-mind 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. In the pretest, 42 percent reported having a positive image of Health Life.

This figure increased to 44 percent in the posttest. Though both key measures increased, the sample sizes for the two tests were relatively small. Random samples of 100 decision makers were used for both tests. Sampling error for the measure of awareness at 95 percent confidence is 8.7 percent. The comparable figure for the image measure is 9.9 percent.

The value used for p in the formula is the posttest result. With these relatively large sampling errors and the relatively small changes in awareness and image, Health Life could only say with 95 percent confidence that awareness in the posttest was 25 percent 8.7 percent, or in the range of 16.3 percent to 33.7 percent. In regard to the image measure, it could only say with 95 percent confidence that the percent of targeted decision makers with a positive image of Health Life in the posttest was 44 percent 9.9 percent, or in the range of 34.1 percent to 53.9 percent.

Based on the relatively small changes in awareness and positive image and the relatively large errors associated with these measures, Health Life could not conclude with any confidence that either measure had actually changed.

The CEO of Health Life is concerned about the amount of money being spent on advertising and wants to know whether the advertising is achieving what it is supposed to achieve. She wants a more sensitive test so that a definitive conclusion regarding the effect of the advertising can be reached.

Question

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 Health Life 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?

Reference no: EM131800718

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