1. If H0 holds, then p̂ in the sample will be less than 0.4.
2. By setting a small a-level, the accounting firm reduces the chance of a test indicating that it should add this new service even though it is not profitable.
3. If p̂ is larger than 0.4, a test will reject the appropriate null hypothesis for this context.
4. The larger the absolute value of the z-statistic that compares p̂ to p, the smaller the p-value.
5. The mean of the sampling distribution of p̂ that is used to determine whether a statistically significant result has been obtained in this example is 0.4.
6. The standard error of the sampling distribution of p̂ depends on an estimate determined from the survey results.
7. The p-value of the test of the null hypothesis in this example is the probability that the firm should add the investment service.
8. Larger samples are more likely than smaller samples to produce a test that incorrectly rejects a true null hypothesis.
An accounting firm is considering offering investment advice in addition to its current focus on tax planning. Its analysis of the costs and benefits of adding this service indicates that it will be profitable if 40% or more of its current customer base use it. The firm plans to survey its customers. Let p denote the proportion of its customers who will use this service if offered, and let p̂ denote the proportion who say in a survey that they will use this service. The firm does not want to invest in this expansion unless data show that it will be profitable.