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Chapter 7: Q2 (page 351)

ComputersIn order to better plan for student resources, the chairperson of the mathematics department at Broward College wants to estimate the percentage of students who own a computer. If we want to estimate that percentage based on survey results, how many students must we survey in order to be 90% confident that we are within four percentage points of the population percentage? Assume that the number of students is very large.

Short Answer

Expert verified

The number of students that must be surveyed to be 90% confident is 423.

Step by step solution

01

Given information

The level of confidence is 90%.

The margin of error is E=0.04.

02

Compute the sample size

The level of confidence is 90%, which implies that the level of significance is 0.10.

From the Z table, the critical value at 0.10 level of significance is 1.645.

Since no prior information on the sample proportion p^is given, the number of students that must be surveyed to be 90% confident is computed as follows:

role="math" localid="1648195763160" n=(zα2)20.25E2=1.6452×0.250.042=422.8≈423

Therefore, the number of students that must be surveyed to be 90% confident is 423.

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Most popular questions from this chapter

Normality Requirement What does it mean when we say that the confidence interval methodsof this section are robust against departures from normality?

Determining Sample Size. In Exercises 31–38, use the given data to find the minimum sample size required to estimate a population proportion or percentage.

Women who give birth An epidemiologist plans to conduct a survey to estimate the percentage of women who give birth. How many women must be surveyed in order to be 99% confident that the estimated percentage is in error by no more than two percentage points?

a. Assume that nothing is known about the percentage to be estimated.

b. Assume that a prior study conducted by the U.S Census Bureau showed that 82% of women give birth.

c. What is wrong with surveying randomly selected adult women?

In Exercises 1–3, refer to the accompanying screen display that results from the Verizon airport data speeds (Mbps) from Data Set 32 “Airport Data Speeds” in Appendix B. The confidence level of 95% was used.

Interpreting a Confidence Interval The results in the screen display are based on a 95%confidence level. Write a statement that correctly interprets the confidence interval.

Years in college Listed below are the numbers of years it took for a random sample of college students to earn bachelor’s degrees (based on the data from the National Center for Education Statistics). Construct a 95% confidence interval estimate of the mean time for all college students to earn bachelor’s degrees. Does it appear that college students typically earn bachelor’s degrees in four years? Is there anything about the data that would suggest that the confidence interval might not be good result?

4 4 4 4 4 4 4.5 4.5 4.5 4.5 4.5 4.5

6 6 8 9 9 13 13 15

Sample Size. In Exercises 29–36, find the sample size required to estimate the population mean.

Mean Pulse Rate of Males Data Set 1 “Body Data” in Appendix B includes pulse rates of 153 randomly selected adult males, and those pulse rates vary from a low of 40 bpm to a high of 104 bpm. Find the minimum sample size required to estimate the mean pulse rate of adult males. Assume that we want 99% confidence that the sample mean is within 2 bpm of the population mean.

a. Find the sample size using the range rule of thumb to estimate σ.

b. Assume that σ=11.3  bpm, based on the value of s=12.5  bpmfor the sample of 153 male pulse rates.

c. Compare the results from parts (a) and (b). Which result is likely to be better?
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