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Chapter 7: Q. 49 (page 454)

Songs on an iPod David’s iPod has about 10000songs. The distribution of the playtimes for these songs is heavily skewed to the right with a mean of 225seconds and a standard deviation of60 seconds. Suppose we choose an SRS of 10 songs from this population and calculate the mean playtime x of these songs. What are the mean and the standard deviation of the sampling distribution of x? Explain.

Short Answer

Expert verified

The mean of the sampling distribution is μx=225seconds

The standard deviation of the sampling distribution isσx=18.9737seconds.

Step by step solution

01

Given information

Total songs =10000

Mean of total songs=225seconds

The standard deviation of total songs=60seconds

the mean and the standard deviation of the sampling distribution of x

02

Explanation

The given data is written as

μ=225seconds

σ=60seconds

n=10

The sample mean x¯is equivalent to the population mean, which is the mean of the sampling distribution.

localid="1650109681905" μx=μ=225seconds

The standard deviation of the sampling distribution of the sample mean xis calculated by dividing the population standard deviation by the square root of the sample size.

localid="1650109697363" σx=σn=6010≈18.9737.

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Most popular questions from this chapter

A grocery chain runs a prize game by giving each customer a ticket that may win a prize when the box is scratched off. Printed on the ticket is a dollar value (\(500,\)100,\(10)or the statement, “This ticket is not a winner.” Monetary prizes can be redeemed for groceries at the store. Here are the distribution of the prize values and the associated probabilities for each prize:

Which of the following are the mean and standard deviation, respectively, of the winnings?
\)15.00,\(2900.00
(b) \)15.00,\(53.85
(c) \)15.00,\(26.9

(d) \)156.25,\(53.85

(e) \)156.25,$26.93

The Gallup Poll has decided to increase the size of its random sample of voters from about 1500people to about 4000people right before an election. The poll is designed to estimate the proportion of voters who favor a new law banning smoking in public buildings. The effect of this increase is to

(a) reduce the bias of the estimate.

(b) increase the bias of the estimate.

(c) reduce the variability of the estimate.

(d) increase the variability of the estimate.

(e) have no effect since the population size is the same

If we take a simple random sample of size n=500from a population of size 5,000,000, the variability of our estimate will be

(a) much less than the variability for a sample of size n=500 from a population of size 50,000,000.

(b) slightly less than the variability for a sample of size n=500from a population of size 50,000,000.

(c) about the same as the variability for a sample of size n=500from a population of size 50,000,000.

(d) slightly greater than the variability for a sample of size n=500from a population of size 50,000,000.

(e) much greater than the variability for a sample of size n=500 from a population of size 50,000,000.

Sale of eggs that are contaminated with salmonella can cause food poisoning in consumers. A large egg producer takes an SRS of 200eggs from all the eggs shipped in one day. The laboratory reports that9of these eggs had salmonella contamination. Unknown to the producer, 0.1%(one-tenth of 1%) of all eggs shipped had salmonella. Identify the population, the parameter, the sample, and the statistic.

A sample of teens A study of the health of teenagers plans to measure the blood cholesterol levels of an SRS of 13- to 16-year-olds. The researchers will report the mean x from their sample as an estimate of the mean cholesterol level M in this population.

(a) Explain to someone who knows no statistics what it means to say that xis an unbiased estimator of μ.

(b) The sample result x is an unbiased estimator of the population mean μ no matter what size SRS the study chooses. Explain to someone who knows no statistics why a large random sample gives more trustworthy results than a small random sample.
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