Discuss the below:
Q1. The Internal Revenue Service is studying contributions to charity. A random sample of 36 returns is selected. The mean contribution is $150 and the standard deviation of the sample is $20. Construct a 98 percent confidence interval for the population mean.
Q2. A manufacturer of batteries for "kids' toys" wishes to investigate the length of time a battery will last. Tests results on a sample of 10 batteries indicated a sample mean of 5.67 and a sample standard deviation of 0.57.
a. Determine the mean and the standard deviation
b. What is the population mean? What is the best estimate of that value?
c. Construct a 95 percent confidence interval for the population mean.
d. Explain why the t distribution is used as a part of the confidence interval.
e. Is it reasonable for the manufacturer to claim that the batteries will last 6.0 hours?
Q3. Refer to Q1. Compute the 98 percent confidence interval if the population consists of 200 tax returns.