# Hypothesis and confidence intervals

(1) A sample of 49 observations is taken from a normal population with a standard deviation of 10. The sample mean is 55. Determine the 99 percent confidence interval for the population mean.

(5) A research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. They found the distribution of amounts spent per week followed the normal distribution with a standard deviation of $5. A sample of 49 steady smokers revealed X= $20

a. What is the point estimate of the population mean? Explain what it indicates.

b. Using the 95 percent level of confidence, determine the confidence interval for _. Explain what it indicates.

(11) 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?

(17) The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy show. Before a final decision is made, network executives commission a sample of 400 viewers. After viewing the comedy, 250 indicated they would watch the new show and suggested it replace the crime investigation show.

a. Estimate the value of the population proportion.

b. Develop a 99 percent confidence interval for the population proportion.

c. Interpret your findings.

(27) A survey is being planned to determine the mean amount of time corporation executives watch television. A pilot survey indicated that the mean time per week is 12 hours, with a standard deviation of 3 hours. It is desired to estimate the mean viewing time within one-quarter hour. The 95 percent level of confidence is to be used. How many executives should be surveyed?

For Exercises 1-4 answer the questions: (a) Is this a one- or two-tailed test? (b) What is the decision rule? (c) What is the value of the test statistic? (d) What is your decision regarding H0? (e) What is the p-value? Interpret it.

(1) The following information is available.

H0: µ = 50

H1: µ ≠ 50

The sample mean is 49, and the sample size is 36. The population standard deviation is 5.

Use the .05 significance level.

(4) A sample of 64 observations is selected from a normal population. The sample mean is

215 and the population standard deviation is 15. Conduct the following test of hypothesis

using the .03 significance level.

H0: µ ≥ 220

H1: µ < 220

(10) Given the following hypothesis:

H0: µ = 400

H1: µ ≠ 400

For a random sample of 12 observations, the sample mean was 407 and the sample

standard deviation 6. Using the .01 significance level:

a. State the decision rule.

b. Compute the value of the test statistic.

c. What is your decision regarding the null hypothesis?

#### Solution Summary

The solution examines hypothesis tests and confidence intervals for normal populations with a standard deviation.