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Chapter 8: Q.2 (page 481)

Got shoes? The class in Exercise 1 wants to estimate the variability in the number of pairs of shoes that female students have by estimating the population variance 蟽2.

Short Answer

Expert verified

The sample variance is s2=202.7658.

Step by step solution

01

Given Information

Data:

02

Explanation

The mean (or average) is the sum of all values divided by the number of values:

x炉=50+26+鈥�+15+5120=30.35

nis the number of values in the data set.

n=20

The sample variance is the sum of squared deviations from the mean divided by n-1:

s2=鈭�(x-x炉)2n-1

(50-30.35)2+(26-30.35)2+(26-30.35)2+(31-30.35)2+(57-30.35)2

+(19-30.35)2+(24-30.35)2+(22-30.35)2+(23-30.35)2+(38-30.35)2

+(13-630.35)2+(50-30.35)2+(13-30.35)2+(34-30.35)2+(23-30.35)2

+(30-30.35)2+(49-30.35)2+(13-30.35)2+(15-30.35)2+(51-30.35)220-1

=202.7658

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Most popular questions from this chapter

5. NAEP scores Young people have a better chance of full-time employment and good wages if they are good with numbers. How strong are the quantitative skills of young Americans of working age? One source
of data is the National Assessment of Educational Progress (NAEP) Young Adult Literacy Assessment Survey, which is based on a nationwide probability sample of households. The NAEP survey includes a
short test of quantitative skills, covering mainly basic arithmetic and the ability to apply it to realistic problems. Scores on the test range from 0to 500. For example, a person who scores 233can add the amounts of two checks appearing on a bank deposit slip; someone scoring 325can determine the price of a meal from a menu; a person scoring 375 can
transform a price in cents per ounce into dollars per pound. Suppose that you give the NAEP test to an SRS of 840people from a large population in which the scores have mean 280and standard deviation蟽=60. The mean xof the 840 scores will vary if you take repeated samples.
(a) Describe the shape, center, and spread of the sampling distribution of x.
(b) Sketch the sampling distribution of x. Mark its mean and the values one, two, and three standard deviations on either side of the mean.
(c) According to the68鈥�95鈥�99.7rule, about 95%of all values of x炉lie within a distance mof the mean of the sampling distribution. What is m? Shade the region on the axis of your sketch that is within m of the mean.

(d) Whenever x炉falls in the region you shaded, the population mean 渭lies in the confidence intervalx卤m. For what percent of all possible samples does the interval capture 渭?

The U.S. Forest Service is considering additional restrictions on the number of vehicles allowed to enter Yellowstone National Park. To assess public reaction, the service asks a random sample of 150 visitors if they favour the proposal. Of these, 89 say 鈥淵es.鈥�

(a) Construct and interpret a 99% confidence interval for the proportion of all visitors to Yellowstone who favours the restrictions.

(b) Based on your work in part (a), can the U.S. Forest Service conclude that more than half of visitors to Yellow-stone National Park favour the proposal? Justify your answer.

Breast-feeding mothers secrete calcium into their milk. Some of the calcium may come from their bones, so mothers may lose bone mineral. Researchers measured the percent change in bone mineral content (BMC) of the spines of 47randomly selected mothers during three months of breastfeeding. The mean change in BMC was -3.587%and the standard deviation was 2.506%.

(a) Construct and interpret a 99%confidence interval to estimate the mean percent change in BMC in the population.

(b) Based on your interval from (a), do these data give good evidence that on average nursing mothers lose bone mineral? Explain.

A Census Bureau report on the income of Americans says that with 90% confidence the median income of all U.S. households in a recent year was \(57,005 with a margin of error of 卤\)742. This means that

(a) 90% of all households had incomes in the range \(57,005 卤\)742.

(b) we can be sure that the median income for all households in the country lies in the range \(57,005 卤\)742.

(c) 90% of the households in the sample interviewed by the Census Bureau had incomes in the range \(57,005 卤\)742.

(d) the Census Bureau got the result \(57,005 卤\)742 using a method that will cover the true median income 90% of the time when used repeatedly.

(e) 90% of all possible samples of this same size would result in a sample median that falls within \(742 of \)57,005.

Teens' online profiles Over half of all American teens (ages 12 to 17 years) have an online profile, mainly on Facebook. A random sample of 487 teens with profiles found that 385 included photos of themselves. 13

(a) Construct and interpret a 95%confidence interval for p. Follow the four-step process.

(b) Is it plausible that the true proportion of American teens with profiles who have posted photos of themselves is 0.75? Use your result from part (a) to support your answer.
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