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Chapter 8: Q.2 (page 522)

It’s critical Find the appropriate critical value for constructing a confidence interval in each of the following settings.

(a) Estimating a population proportion p at a 94%confidence level based on an SRS of size 125.

(b) Estimating a population mean M at a 99%confidence level based on an SRS of size 58.

Short Answer

Expert verified

a). The critical value is 1.96.

b). The critical value is 2.576.

Step by step solution

01

Part (a) Step 1: Given Information

Population proportion (p)=94%=0.94.

Sample size (n)=125.

02

Part (a) Step 2: Explanation

The level of significance is:

Level of significance =1-Confidence level

=1-0.95

=0.05

The critical value using standard normal table is calculated as:

zα/2=z0.05/2

=z0.025

=1.96

The critical value is 1.96.

03

Part (b) Step 1: Given Information

Confidence level =99%.

Sample size (n)=58.

04

Part (b) Step 2: Explanation

The level of significance is:

Level of significance =1-Confidence level

=1-0.99

=0.01

The critical value using the standard normal table is calculated as:

za/2=z0.01/2

=z0.005

=2.576

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Most popular questions from this chapter

Running red lights A random digit dialing telephone survey of880drivers asked, "Recalling the last ten traffic lights you drove through, how many of them were red when you entered the intersections?" Of the 880respondents, 171admitted that at least one light had been red.15

(a) Construct and interpret a95%confidence interval for the population proportion.

(b) Nonresponse is a practical problem for this survey-only 21.6%of calls that reached a live person were completed. Another practical problem is that people may not give truthful answers. What is the likely direction of the bias: do you think more or fewer than 171of the 880respondents really ran a red light? Why? Are these sources of bias included in the margin of error?

Equality for women? Have efforts to promote equality for women gone far enough in the United States? A poll on this issue by the cable network MSNBC contacted 1019adults. A newspaper article about the poll said, “Results have a margin of sampling error of plus or minus 3 percentage points.”15

(a) The news article said that 65% of men, but only 43% of women, think that efforts to promote equality have gone far enough. Explain why we do not have enough information to give confidence intervals for men and women separately.

(b) Would a 95% confidence interval for women alone have a margin of error less than 0.03, about equal to 0.03, or greater than 0.03? Why? (You see that the news article’s statement about the margin of error for poll results is a bit misleading.)

One reason for using a tdistribution instead of the standard Normal curve to find critical values when calculating a level C confidence interval for a population mean is that

(a) zcan be used only for large samples.

(b) zrequires that you know the population standard deviation σ.

(c) zrequires that you can regard your data as an SRS from the population.

(d) the standard Normal table doesn't include confidence levels at the bottom.

(e) a zcritical value will lead to a wider interval than a tcritical value.

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Behavioral Surveys sample of 2673adult heterosexuals, 0.2%had both received a blood transfusion and had a sexual partner from a group at high risk of A I D S. We want to estimate the proportion pin the population who share these two risk factors.

57. Critical values What critical value t* from Table B would you use for a confidence interval for the population mean in each of the following situations?
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