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Chapter 9: Q.11.48 (page 460)

We have specified a margin of error, a confidence level, and a likely range for the observed value of the sample proportion. For each exercise, obtain a sample size that will ensure a margin of error of at most the one specified (provided of course that the observed value of the sample proportion is further from 0.5than the educated guess).Obtain a sample size that will ensure a margin of error of at most the one specified.

marginoferror=0.04;confidencelevel=99%;likelyrange=0.7orless

Short Answer

Expert verified

A sample size that will ensure a margin of error of at most the one specified.is approximately1,037

Step by step solution

01

step1: Given information

When the margin of error is 0.04 and the confidence level is 99% , calculate the sample size.

02

calculation

When the margin of error is 0.04and the confidence level is 99%, we can calculate the sample size.

With a 99%confidence level, the required value of localid="1651496589910" zα/2from table areas under the standard normal curve is 2.575

Use localid="1651496594165" p'g=.05Because the value in the range is close to 0.5.

The sample size for this study is,

localid="1651496599039" n=0.25za_2E2=0.252.5750.042=0.25(4,144.14)=1,036.04≈1,037

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Most popular questions from this chapter

Testing Claims About Proportions. In Exercises 7–22, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.

Dreaming in Black and White A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 306 people over the age of 55, 68 dream in black and white, and among 298 people under the age of 25, 13 dream in black and white (based on data from “Do We Dream in Color?” by Eva Murzyn, Consciousness and Cognition, Vol. 17, No. 4). We want to use a 0.01 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion of those under 25.

a. Test the claim using a hypothesis test.

b. Test the claim by constructing an appropriate confidence interval.

c. An explanation given for the results is that those over the age of 55 grew up exposed to media that was mostly displayed in black and white. Can the results from parts (a) and (b) be used to verify that explanation?

Confidence Interval for Haemoglobin

Large samples of women and men are obtained, and the haemoglobin level is measured in each subject. Here is the 95% confidence interval for the difference between the two population means, where the measures from women correspond to population 1 and the measures from men correspond to population 2: -1.76g/dL<μ1-μ2<-1.62g/dL.

a. What does the confidence interval suggest about equality of the mean hemoglobin level in women and the mean hemoglobin level in men?

b. Write a brief statement that interprets that confidence interval.

c. Express the confidence interval with measures from men being population 1 and measures from women being population 2.

Braking Reaction Times: Histogram Listed below are sorted braking reaction times (in 1>10,000 sec) for male and female subjects (based on data from the RT-2S Brake Reaction Time Tester). Construct a histogram for the reaction times of males. Use a class width of 8 and use 28 as the lower limit of the first class. For the horizontal axis, use class midpoint values. Does it appear that the data are from a population with a normal distribution?

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Testing Claims About Proportions. In Exercises 7–22, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.

Clinical Trials of OxyContin OxyContin (oxycodone) is a drug used to treat pain, butit is well known for its addictiveness and danger. In a clinical trial, among subjects treatedwith OxyContin, 52 developed nausea and 175 did not develop nausea. Among other subjectsgiven placebos, 5 developed nausea and 40 did not develop nausea (based on data from PurduePharma L.P.). Use a 0.05 significance level to test for a difference between the rates of nauseafor those treated with OxyContin and those given a placebo.

a. Use a hypothesis test.

b. Use an appropriate confidence interval.

c. Does nausea appear to be an adverse reaction resulting from OxyContin?

Denomination Effect Construct the confidence interval that could be used to test the claim in Exercise 1. What feature of the confidence interval leads to the same conclusion from Exercise 1?
See all solutions

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