The National Collegiate Athletic Association (NCAA) reported that the mean number of hours spent per week on coaching and recruiting by college football assistant coaches during the season was 70. A random sample of 50 assistant coaches showed the sample mean to be 68.6 hours, with a standard deviation of 8.2 hours.
a. Using the sample data, construct a 99% confidence interval for the population mean.
b. Does the 99% confidence interval include the value suggested by the NCAA? Interpret this result.
c. Suppose you decide to switch from a99% to 95% confidence interval. Without performing any calculations, will the interval increase, decrease, or stay the same? Which of the values in the formula will change?
Dr. Susan Benner is an industrial psychologist. She is currently studying stress among executives of Internet companies. She developed a questionnaire that she believes measures stress. A score above 80 indicates stress at a dangerous level. A random sample of 15 executives revealed the following stress level scores.
a. Find the mean stress level for this sample. What is the point estimate of the population?
b. Construct a 95 % confidence level for the population mean.
c. Is it reasonable to conclude that Internet executives have a mean stress level in the dangerous level, according to Dr. Benner’s test?
Problem # 50
Families USA, a monthly magazine that discusses issues related to health and health costs, surveyed 20 of its subscribers. It found that the annual health insurance premiums for a family with coverage through an employer averaged $10,979. The standard deviation of the sample was $1,000.
a. Based on this sample information, develop a 90% confidence interval for the population mean yearly premium.
b. How large a sample is needed to find the population mean within $250 at 99% confidence?
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