# Statistical Problems - Mean, Confidence Interval, Testing

1. The owner of Britten's Egg Farm wants to estimate the mean number of eggs laid per chicken. A sample of 20 chickens shows they laid an average of 20 eggs per month with a standard deviation of 2 eggs per month.

a. What is the value of the population mean? What is the best estimate of this value?

b. Explain why we need to use the t distribution. What assumption do you need to make?

c. For a 95 percent confidence interval, what is the value of t?

d. Develop the 95 percent confidence interval for the population mean.

e. Would it be reasonable to conclude that the population mean is 21 eggs? What about 25 eggs?

2. 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 is 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 percent confidence interval for the population mean.

b. Does the 99 percent confidence interval include the value suggested by the NCAA? Interpret this result.

c. Suppose you decided to switch from a 99 to a 95 percent confidence interval. Without performing any calculations, will the interval increase, decrease, or stay the same? Which of the values in the formula will change?

#### Solution Preview

1. The owner of Britten's Egg Farm wants to estimate the mean number of eggs laid per chicken. A sample of 20 chickens shows they laid an average of 20 eggs per month with a standard deviation of 2 eggs per month.

a. What is the value of the population mean? What is the best estimate of this value?

The value of the population mean is guessed to be normally distributed around the sample mean of 20 eggs/month. However, egg laying may be better characterized by a Poisson distribution. But that was not the intent of the instructor in asking part a. The best estimate of the value is 20 eggs/month with the sampling performed to this point.

b. Explain why we need to use the t distribution. What assumption do you need to make?

The sample population is less than the magic number of 30. If we indeed have a normal population than for n small, the sample size, the set of all means for samples of size n is still normally distributed, but the ...

#### Solution Summary

This solution is provided in approximately 737 words. It discusses how to calculate mean and confidence interval, and makes conclusions about each study.