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Chapter 8: Q. 75 (page 520)

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 蟽.

(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.

Short Answer

Expert verified

(b) z requires that you know the population standard deviation 蟽.

Step by step solution

01

Given Information

(a) zcan be used only for large samples.

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

(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.

02

Explanation

(a) False, zcan also be used for small samples from a Normal population.

(b) True, if you know the population standard deviation 蟽, then you use the z-procedure, else you use the t-procedure.

(c) False, a random sample instead of a simple random sample is also sufficient.

(d) False, you can still determine the critical value using the standard Normal table.

(e) False, the procedure to be used is not dependent on the width of the interval.

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Most popular questions from this chapter

Explain briefly why each of the three conditions鈥擱andom, Normal, and Independent鈥攊s important when constructing a confidence interval.

Election polling Gloria Chavez and Ronald Flynn are the candidates for mayor in a large city. We want to estimate the proportion pof all registered voters in the city who plan to vote for Chavez with 95% con铿乨ence and a margin of error no greater than 0.03. How large a random sample do we need? Show your work.

A polling organization announces that the proportion of American voters who favor congressional term limits is 64%, with a 95%confidence margin of error of 3%. If the opinion poll had announced the margin of error for 80% confidence rather than 95%confidence, this margin of error would be

(a) 3%, because the same sample is used.

(b) less than 3%, because we require less confidence.

(c) less than 3%, because the sample size is smaller.

(d) greater than 3%, because we require less confidence.

(e) greater than 3%, because the sample size is smaller.

Use Table B to find the critical value t* that you would use for a confidence interval for a population mean M in each of the following situations. If possible, check your answer with technology.

(a) A 98% confidence interval based on n=22observations.

(b) A 90%confidence interval from an SRS of 10observations.

(c) A 95% confidence interval from a sample of size7.

How many people live in South African households? To find out, we collected data from an SRS of 48 out of the over 700,000 South African students who took part in

the CensusAtSchool survey project. The mean number of people living in a household was 6.208; the standard deviation was 2.576.

(a) Is the Normal condition met in this case? Justify your answer.

(b) Maurice claims that a 95% confidence interval for the population mean is 6.208卤1.960.37247. Explain why this interval is wrong. Then give the correct interval.
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