Mixed Examples of Hypothesis Testing Confidence Intervals Example

Mixed Examples of Hypothesis Testing & Confidence Intervals

Example 1 �An insurance company is reviewing its current policy rates. When originally setting the rates they believed that the average claim amount was $1, 800. They are concerned that the true mean is actually higher than this, because they could potentially lose a lot of money. They randomly select 40 claims, and calculate a sample mean of $1, 950. Assuming that the standard deviation of claims is $500, and set α =. 05, test to see if the insurance company should be concerned.

Example 2 �A Gallup poll asked Americans to rate their life on a scale of 0 to 10 (0 being the worst possible life and 10 being the best). The 1, 000 people who have a television set reported a mean of 6. 07 with a standard deviation of 1. 1. Of the 300 people without a television set, the mean score was 4. 47 with a standard deviation of 2. 8. http: //www. gallup. com/poll/105850/Ownership-May-Good-Well. Being. aspx �Form a 90% confidence interval for the mean difference.

Example 3 �Suppose the Acme Drug Company develops a new drug, designed to prevent colds. The company states that the drug is equally effective for men and women. To test this claim, they chose a simple random sample of 100 women and 200 men from a population of 100, 000 volunteers. �At the end of the study, 38% of the women caught a cold; and 51% of the men caught a cold. Based on these findings, can we reject the company's claim that the drug is equally effective for men and women? Use a 0. 05 level of significance.

Example 4 � A hospital wants to get an estimate for infection rates of patients coming out of surgery. They observe a random sample of 120 patients who come out of surgery and find that 15 of them develop an infection while recovering. � Construct a 95% confidence interval for the infection rate at this hospital. � Explain what this confidence interval means. � If the hospital wanted to narrow its confidence interval, what should it do?

Example 5 �A sample of 40 sales receipts from a grocery store has a mean of $137 and a standard deviation of $30. 2. Use these values to test whether or not the mean sales at the grocery store is less than $150.