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Chapter 8: Q.9 (page 477)

Construct a 90% confidence interval for the population mean time to complete the forms. State the confidence interval, sketch the graph and calculate the error bound.

Short Answer

Expert verified

The confidence interval isCl:(7.9441,8.4559).

Step by step solution

01

Given Information

90% confidence interval for the population mean time to complete the forms.

02

Explanation

Let's calculate the Margin of error by using the given formula:

Za2脳蟽n

Place the values=Z0.102脳2.2200=1.6449脳2.2200=0.25588

Then we have to find the confidence interval by using the given formula:

X炉卤Za2脳蟽n

role="math" localid="1652508772667" Confidence Interval=8.2卤Z0.102脳2.2200=8.2卤1.6449脳2.2200=[7.944,8.455]

Therefore, the confidence interval Cl:(7.9441,8.4559).

The graph:

The error bound EBM=0.26.

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Most popular questions from this chapter

A camp director is interested in the mean number of letters each child sends during his or her camp session. The

population standard deviation is known to be 2.5. A survey of 20campers is taken. The mean from the sample is 7.9with a

sample standard deviation of 2.8.

a.

localid="1651507797100" i.x虅=________ii.蟽=________iii.n=________

b. Define the random variables XandX虅

in words.

c. Which distribution should you use for this problem? Explain your choice.

d. Construct a 90%confidence interval for the population mean number of letters campers send home.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

e. What will happen to the error bound and confidence interval if 500campers are surveyed? Why?

On May 23,2013, Gallup reported that of the 1005people surveyed, 76%of U.S. workers believe that they will continue working past retirement age. The confidence level for this study was reported at 95%with a 卤3%margin of error.

a. Determine the estimated proportion from the sample.

b. Determine the sample size.

c. Identify CL and .

d. Calculate the error bound based on the information provided.

e. Compare the error bound in part d to the margin of error reported by Gallup. Explain any differences between the values.

f. Create a confidence interval for the results of this study.

g. A reporter is covering the release of this study for a local news station. How should she explain the confidence interval to her audience?

The U.S. Census Bureau conducts a study to determine the time needed to complete the short form. The Bureau surveys 200 people. The sample mean is 8.2 minutes. There is a known standard deviation of 2.2 minutes. The population distribution is assumed to be normal.

Identify the following:

a. x炉 = _____

b. 蟽 = _____

c. n = _____

Announcements for 84 upcoming engineering conferences were randomly picked from a stack of IEEE Spectrum

magazines. The mean length of the conferences was 3.94 days, with a standard deviation of 1.28 days. Assume the

underlying population is normal.

a. In words, define the random variables X and X

b. Which distribution should you use for this problem? Explain your choice.

c. Construct a 95% confidence interval for the population mean length of engineering conferences.

I. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

Using the same mean, standard deviation, and sample size, how would the error bound change if the confidence level were reduced to 90%? Why?
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