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Chapter 8: Q 8.7RP. (page 346)

A confidence interval for a population mean has a margin of error of 10.7

a. Obtain the length of the confidence interval.

b. If the mean of the sample is 75.2, determine the confidence interval.

Short Answer

Expert verified

Part (a) 21.4

Part (b) (64.5,85.9)

Step by step solution

01

Part (a) Step 1: Given information

The margin of error for a population mean confidence interval is10.7

02

Part (a) Step 2: Concept

The formula used: Length of the Cl for population mean =2脳 margin of error

03

Part (a) Step 3: Calculation

Margin of error E=10.7

We know that,

Cllength for the population mean=2脳 margin of error

=2脳10.7=21.4
04

Part (b) Step 1: Calculation

Given that, the sample mean x炉=75.2

The confidence interval of the population mean

=(x炉-E,x炉+E)=(75.2-10.7,75.2+10.7)=(64.5,85.9)

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Most popular questions from this chapter

A confidence interval for a population mean has length 20.

a. Determine the margin of error.

b. If the sample mean is 60, obtain the confidence interval.

c. Construct a graph that illustrates your results.

Formula 8.2on page 327provides a method for computing the sample size required to obtain a confidence interval with a specified confidence level and margin of error. The number resulting from the formula should be rounded up to the nearest whole number.

a. Why do we want a whole number?

b. Why do we round up instead of down?

Express the form of most of the confidence intervals that you will encounter in your study of statistics in terms of "point estimate" and "margin of error."

A confidence interval for a population mean has a margin of error of 0.047

a. Determine the length of the confidence interval.

b. If the sample mean is 0.205, obtain the confidence interval.

c. Construct a graph that illustrates your results.

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 outliers, and the sample size is20.
See all solutions

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