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Chapter 8: Q.9 (page 482)

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

Short Answer

Expert verified

The nearest confidence level is 80%.

Step by step solution

01

Given Information

The result of 25SRSs:

02

Explanation

The red lines under the curve represent the sample means that does not contain the true population mean 渭.

We note that there are 4out of the 25samples that do not contain the true proportion and thus 21out of the 25samples contain the true mean:

2125=0.84=84%

The nearest confidence level is 80%

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Most popular questions from this chapter

Good wood? A lab supply company sells pieces of Douglas fir 4inches long and 1.5inches square for force experiments in science classes. From experience, the strength of these pieces of wood follows a Normal distribution with standard deviation 3000pounds. You want to estimate the mean load needed to pull apart these pieces of wood to within 1000pounds with 95%confidence. How large a sample is needed? Show your work.

- Understand how the margin of error of a confidence interval changes with the sample size and the level of confidence C.

Teens" online profiles Describe a possible source of error that is not included in the margin of error for the 95% confidence interval in Exercise 36

Abstain from drinking In a Harvard School of Public Health survey, 2105 of 10,904 randomly selected U.S. college students were classified as abstainers (nondrinkers).

(a) Construct and interpret a 99% confidence interval forp. Follow the four-step process.

(b) A newspaper article claims that 25% of U.S. college students are nondrinkers. Use your result from (a) to comment on this claim.

School vouchers A national opinion poll found that 44% of all American adults agree that parents should be given vouchers that are good for education at any public or private school of their choice. The result was based on a small sample.

(a) How large an SRS is required to obtain a margin of error of 0.03(that is, 卤3%) in a 99% con铿乨ence interval? Answer this question using the previous poll鈥檚 result as the guessed value for p鈭�.

(b) Answer the question in part (a) again, but this time use the conservative guess p鈭�=0.5. By how much do the two sample sizes differ?

The Gallup Poll interviews 1600people. Of these, 18%say that they jog regularly. The news report adds: "The poll had a margin of error of plus or minus three percentage points at a 95%confidence level." You can safely conclude that

(a) 95%of all Gallup Poll samples like this one give answers within卤3%of the true population value.

(b) the percent of the population who jog is certain to be between 15%and21%.

(c) 95%of the population jog between5%and21%of the time.

(d) we can be 95%confident that the sample proportion is captured by the confidence interval.

(e) if Gallup took many samples,95%of them would find that 18%of the people in the sample jog.
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