# Null & Alternative Hypotheses

In hypothesis testing, the null hypothesis is tested and a decision is made as to whether to reject or not reject the null hypothesis. Then the conclusion must be stated in terms of the problem being studied. Determining the null and alternate hypotheses sometimes presents problems for students. This discussion activity will give you some practice at that, and an opportunity to discuss it with others in the class.

Example: More professional women than ever before are foregoing motherhood because of the time constraints of their careers. Yet, many women still manage to find time to climb the corporate ladder and set time aside to have children. At the .05 level of significance, can you state that more than half of all successful women executives have children? Assuming that the null hypothesis is not rejected, state the conclusion in terms of the problem.

Solution: The population parameter of interest is the proportion. The question asks if more than half of all successful women executives have children. That would be p > 0.5 and, since it doesnÃ¢Ã¢?Â¬Ã¢?Â¢t contain the equal sign it would be the alternate hypothesis. (Remember that the alternate hypothesis never contains the equal sign. The null hypothesis always contains the equal sign.) Then the null hypotheses would be p <= 0.5. Remember that the conclusion is normally stated in terms of the alternate hypothesis. If the null hypothesis is not rejected in this problem, the conclusion would be that at the .05 level of significance, there is no evidence that more than half of all successful women executives have children.

For each of the questions below state the null and alternate hypotheses. (Be sure to state them in terms of the population parameter of interest.) Then state the conclusion in terms of the problem. (NOTE: You arenÃ¢Ã¢?Â¬Ã¢?Â¢t given enough information to actually do the hypotheses tests in the problems below.)

1. At the .01 level of significance, is there evidence that less than half of the employed workforce in the United States has Internet access at work? State the null and alternate hypothesis. Assuming that the null hypothesis is rejected, state the conclusion in terms of the problem.

2. In New York State, savings banks are permitted to sell a form of life insurance called Savings Bank Life Insurance (SBLI). The approval process consists of underwriting, which includes a review of the application, a medical information bureau check, possible requests for additional medical information and medical exams, and a policy compilation stage in which the policy pages are generated and sent to the bank for delivery. The ability to deliver approved policies to customers in a timely manner is critical to the profitability of this service to the bank. At the .05 level of significance, is there evidence that the mean processing time is different than 45 days? State the null and alternate hypothesis. Assuming that the null hypothesis is not rejected, state the conclusion in terms of the problem.

3. A manufacturing company produces electrical insulators. If the insulators break when in use, a short circuit is likely to occur. To test the strength of the insulators, destructive testing is carried out to determine how much force is required to break the insulators. Force is measured by observing how many pounds are applied to the insulator before it breaks. At the .05 level of significance, is there evidence that the mean force is greater than 1500 pounds? State the null and alternate hypothesis. Assuming that the null hypothesis is rejected, state the conclusion in terms of the problem.

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#### Solution Summary

The solution provides null and alternative hypotheses and conclusion for hypothesis testing problems.