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Construct a confidence interval at the given level for the population mean based on the sample mean. Each question is worth 10 points. Make sure to answer the question at the end of each item.
Use the formula: sample mean margin of error Margin of error = zc
1. A manager of a baseball stadium wished to construct a 90% confidence interval for the average age of all baseball fans. In a random sample of 40 fans, the mean age was 32.5 years with a standard deviation of 2.3 years. Construct the interval. Why would the manager find this information useful?

2. A random sample of 42 computers has an average price of $875 with a standard deviation of $54. The principal of a high school wants to construct a 95% confidence interval for the average price. Construct the interval for her. Why would the principal find this information useful?

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3. The school nurse surveys 30 girls and finds the average weight of these girls to be 134 pounds with a standard deviation of 12 pounds. Construct a 99% confidence interval for the nurse and tell how she might use this information.

4. A random sample of 36 cats found the average weight to be 9.8 pounds with a standard deviation of 2.4 pounds.
a. Construct a 90% confidence interval for the average weight of the cats.

b. Construct a 95% confidence interval for the average weight of the cats.

c. How and why did the intervals change?

5. A consumer is considering purchasing a set of tires. She samples 30 companies and finds the average price of a set of tires is $245 with a standard deviation of $38. Construct a 95% confidence interval for the average price of the tires. How would this information help her in purchasing the tires?

If she samples 50 companies, how and why does the interval change?

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