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Chapter 8: Q. 51 (page 498)

51. You want to design a study to estimate the proportion of students at your school who agree with the statement, 鈥淭he student government is an effective organization for expressing the needs of students to the administration.鈥� You will use a 95% confidence interval, and you would like the margin of error to be 0.05 or less. The minimum sample size required is
(a) 22. (b) 271. (c) 385. (d) 769. (e) 1795.

Short Answer

Expert verified

The correct answer is option (c) 385.

Step by step solution

01

Given information

To find the minimum sample size required for 95%confidence interval, and the margin of error to be 0.05 or less.

02

Explanation

Let, mirror of error is E=0.05.

Determine the sample size as:

p^unknown: n=z伪/220.25E2

Using table A, for confidence level 95%,
z伪/2=1.96
p^ is unknown, then the sample size is:
n=z伪/220.25E2

=1.962脳0.250.052

鈮�385

As a result, option (c) 385 is correct.

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Most popular questions from this chapter

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

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.

To assess the accuracy of a laboratory scale, a standard weight known to weigh 10grams is weighed repeatedly. The scale readings are Normally distributed with unknown mean (this mean is 10grams if the scale has no bias). In previous studies, the standard deviation of the scale readings has been about 0.0002gram. How many measurements must be averaged to get a margin of error of 0.0001with 98% confidence? Show your work.

An online poll posed the following question:

It is now possible for school students to log on to Internet sites and download homework. Everything from book reports to doctoral dissertations can be downloaded free or for a fee. Do you believe that giving a student who is caught plagiarizing an F for their assignment is the right punishment?

Of the 20,125people who responded, 14,793clicked 鈥淵es.鈥� That鈥檚 73.5%of the sample. Based on this sample, a 95%confidence interval for the percent of the population who would say 鈥淵es鈥� is 73.5% 卤0.61. Which of the three inference conditions is violated? Why is this confidence interval worthless?

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.
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