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Chapter 8: Q 8.68. (page 331)

In each of Exercises 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.l on page 325

x=55,n=16,蟽=5, confidence level =99%

Short Answer

Expert verified

Part (a) The 90%confidence interval for 渭is (51.7812,58.2188)

Part (b) The margin of error by using the half-length of the confidence interval is3.2188

Part (c) The margin of error by using the formula is3.2188

Step by step solution

01

Part (a) Step 1: Given information

x=55,n=16,蟽=5, confidence level =99%

02

Part (a) Step 2: Concept

The formula used: the confidence intervalx炉卤z伪2蟽nandMarginof error(E)=za2蟽n

03

Part (a) Step 3: Calculation

Compute the 90%confidence interval for 渭

Consider x炉=55,n=16,蟽=5, and confidence level is 90%

The needed value of za2 with a 90% confidence level is 2.575, as shown in "Table II Areas under the standard normal curve."

Thus, the confidence interval is,

x炉卤z伪2蟽n=55卤2.575516=55卤2.575(1.25)=55卤3.2188=(51.7812,58.2188)

Therefore, the 99% confidence interval for 渭 is (51.7812,58.2188)

04

Part (b) Step 1: Calculation

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

Margin of error=58.2188-51.78122=6.43762=3.2188

Thus, the margin of error by using the half-length of the confidence interval is 3.2188

05

Part (c) Step 1: Calculation

Using a formula, calculate the margin of error.

Margin of error(E)=za2蟽n=2.575516=2.575(1.25)=3.2188

The margin of error by using the formula is 3.2188

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Most popular questions from this chapter

Civilian Labor Force. Consider again the problem of estimating the mean age, 渭, of all people in the civilian labor force. In Example 8.7on page 328 , we found that a sample size of 2250 is required to have a margin of error of 0.5year and a 95% confidence level. Suppose that, due to financial constraints, the largest sample size possible is 900 . Determine the smallest margin of error, given that the confidence level is to be kept at 95%. Recall that蟽=12.1 years.

Digital Viewing Times. Refer to Exercise 8.130

a. Find and interpret a 90%lower confidence bound for last year's mean time spent per day with digital media by American adults.

b. Compare your one-sided confidence interval in part (a) to the (two-sided) confidence interval found in Exercise 8.130.

For a t-curve with df=8, find each t-value, and illustrate your results graphically.

a. The t-value having area 0.05 to its right

b. t0.10

c. The t-value having area 0.01 to its left (Hint: A t-curve is symmetric about 0

d. The two t-values that divide the area under the curve into a middle 0.95 area and two outside 0.025 areas

Poverty and Dietary Calcium. Refer to Exercise 8.70

a. Determine and interpret a 95%upper confidence bound for the mean calcium intake of all people with incomes below the poverty level.

b. Compare your one-sided confidence interval in part (a) to the (twosided) confidence interval found in Exercise 8.70

A variable has a mean of 100 and a standard deviation of 16 Four observations of this variable have a mean of 108 and a sample standard deviation of 12 . Determine the observed value of the

a. standardized version of x炉.

b. studentized version of x炉.
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