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Chapter 7: Q. 38 (page 440)

Do you go to church? What sample size would be required to reduce the standard deviation of the sampling distribution to one-third the value you found in Exercise 36 (b)? Justify your answer.

Short Answer

Expert verified

The sample size of16,065would be required to reduce the standard deviation of the sampling distribution to one-third the value.

Step by step solution

01

Given Information

Sample size =1785

Proportion of condition=10%

02

Explanation 

We have,

n=1785

The standard deviation formula is

σp^=p(1-p)n

Assuming the standard deviation should become one third of the current standard deviation:

localid="1650086930094" σp^3=13×p(1−p)n=p(1−p)9n

Multiplying the sample size by 9 will yield the following result:

localid="1650086939099" 9n=9(1785)n=16065

Hence, a new sample size of 16065is needed

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Most popular questions from this chapter

What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the histogram of the sample values looks mote and more Normal." ls the student right? Explain your answer.

The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. When traps are checked periodically, the mean number of moths trapped is only 0.5,but some traps have several moths. The distribution of moth counts is discrete and strongly skewed, with standard deviation0.7.

(a) What are the mean and standard deviation of the average number of moths xin50traps?

(b) Use the central limit theorem to help you find the probability that the average number of moths in 50traps is greater than0.6.

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.

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

For Exercises 1 to 4, identify the population, the parameter, the sample, and the statistic in each setting.

Gas prices How much do gasoline prices vary in a large city? To find out, a reporter records the price per gallon of regular unleaded gasoline at a random sample of 10gas stations in the city on the same day. The range (maximum-minimum) of the prices in the sample is 25cents

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