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Chapter 8: Q 8.66. (page 331)

In each exercise 8.63-8.68, we provide a sample mean, sample size, population standard deviation, and confidence level. In each case, perform the following tasks:

a. Use the one-mean z-interval procedure to find a confidence interval for the mean of the population from which the sample was drawn.

b. Obtain the margin of error by taking half the length of the confidence interval.

c. Obtain the margin of error by using Formula 8.1 on page 325

x炉=35,n=25,蟽=4, confidence level =90%

Short Answer

Expert verified

Part (a) the 90% confidence interval for 渭 is (33.684,36.316)

Part (b) The margin of error by using the half length of the confidence interval is 1.316

Part (c) The margin of error by using formula is 1.316

Step by step solution

01

Part (a) Step 1: Given information

x炉=35,n=25,蟽=4, confidence level =90%

02

Part (a) Step 2: Concept

The formula used: the confidence intervalx炉卤za2蟽nandMargin of error(E)=za2蟽n

03

Part (a) Step 3: Calculation

Compute the 90%confidence interval for渭

The needed value of z伪2 with a 90%confidence level is 1.645 as shown in "Table II Areas under the standard normal curve."

Thus, the confidence interval is,

x炉卤z伪2蟽n=35卤1.645425=35卤1.645(0.8)=35卤1.316=(33.684,36.316)

Therefore, the 90%confidence interval for 渭is (33.684,36.316)

04

Part (b) Step 1: Calculation

Using the half-length of the confidence interval, calculate the margin of error.

Margin of error=36.316-33.6842=2.6322=1.316

Thus, the margin of error by using the half-length of the confidence interval is 1.316

05

Part (c) Step 1: Calculation

Using a formula, calculate the margin of error.

Margin oferror(E)=za2蟽n=1.645425=1.645(0.8)=1.316

Thus, the margin of error by using the formula is 1.316

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Most popular questions from this chapter

American Alligators. Refer to Exercise 8.78.

a. Determine the margin of error for the 95%confidence interval.

b. Determine the margin of error for the 99%confidence interval.

c. Compare the margins of error found in parts (a) and (b).

d. What principle is being illustrated?

Corporate Farms. The U.S. Census Bureau estimates the mean value of the land and buildings per corporate farm. Those estimates are published in the Census of Agriculture, Suppose that an estimate, x, is obtained and that the margin of error is \(1000. Does this result imply that the true mean. 渭, is within \)1000 of the estimate? Explain your answer.

Bicycle Commuting Times. A city planner working on bikeways designs a questionnaire to obtain information about local bicycle commuters. One of the questions asks how long it takes the rider to pedal from home to his or her destination. A sample of local bicycle commuters yields the following times, in minutes.

a. Find a 90%confidence interval for the mean commuting time of all local bicycle commuters in the city. (Note: The sample mean and sample standard deviation of the data are 25.82minutes and 7.71minutes, respectively.)

b. Interpret your result in part (a).

c. Graphical analyses of the data indicate that the time of 48min utes may be an outlier. Remove this potential outlier and repeat part (a). (Note: The sample mean and sample standard deviation of the abridged data are 24.76 and 6.05, respectively.)

d. Should you have used the procedure that you did in part (a)? Explain your answer.

Assume that the population standard deviation is known and decide weather use of the z-interval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers .

The sample data contain no outliers, the sample size is 250, and the variable under consideration is far from being normally distributed.

What is meant by saying that a statistical procedure is robust?
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