1. Mixed Examples of Hypothesis Testing & Confidence Intervals

2. 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.

3. 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.
Form a 90% confidence interval for the mean difference.

4. 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.

5. 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?

6. 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.