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How confident? The figure at top right shows the result of taking 25SRSs from a Normal population and constructing a confidence interval for each sample. Which confidence level—80%,90%,95%, or 99%—do you think was used? Explain.

Short Answer

Expert verified

The nearest confidence level is 99%.

Step by step solution

01

Given Information

The result of taking 25 SRSs:

02

Explanation

The red lines under the curve represent the sample means that do not contain the true population proportion.

We note that there are 0out of the 25samples that do not contain the true proportion and thus 25out of the 25samples contain the true proportion:

2525=1=100%

The nearest confidence level is 99%(although 95%could also be a possible used confidence level).

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Most popular questions from this chapter

High tuition costs Glenn wonders what proportion of the students at his school think that tuition is too high. He interviews an SRS of 50 of the 2400 students at his college. Thirty-eight of those interviewed think tuition is too high.

A telephone poll of an SRS of 1234 adults found that 62% are generally satisfied with their lives. The announced margin of error for the poll was 3%. Does the margin of

error account for the fact that some adults do not have telephones?

(a) Yes. The margin of error includes all sources of error in the poll.

(b) Yes. Taking an SRS eliminates any possible bias in estimating the population proportion.

(c) Yes. The margin of error includes under coverage but not nonresponse.

(d) No. The margin of error includes nonresponse but is not under coverage.

(e) No. The margin of error only includes sampling variability.

Many television viewers express doubts about the validity of certain commercials. In an attempt to answer their critics, Timex Group USA wishes to estimate the proportion of consumers who believe what is shown in Timex television commercials. Let prepresent the true proportion of consumers who believe what is shown in Timex television commercials. What is the smallest number of consumers that Timex can survey to guarantee a margin of error of 0.05or less at a 99%confidence level?

(a) 550

(b) 600

(c) 650

(d) 700

(c)750

I collect an SRS of size n from a population and compute a 95%confidence interval for the population proportion. Which of the following would produce a new confidence interval with larger width (larger margin of error) based on these same data?

(a) Use a larger confidence level.

(b) Use a smaller confidence level.

(c) Increase the sample size.

(d) Use the same confidence level, but compute the interval n times. Approximately5% of these intervals will be larger.

(e) Nothing can guarantee absolutely that you will get a larger interval. One can only say that the chance of obtaining a larger interval is 0.05.

Critical value What critical value t*from Table B would you use for a 90%confidence interval for the population mean based on an SRS of size 77? If possible, use technology to find a more accurate value of . What advantage does the more accurate df provide?

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