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Chapter 11: Q.4 (page 480)

Fill in the blanks.

a. The mean of all possible sample proportions is equal to the

b. For large samples, the possible sample proportions have approximately a distribution.

c. A rule of thumb for using a normal distribution to approximate the distribution of all possible sample proportions is that both and are or greater.

Short Answer

Expert verified

a). The mean of sample proportions is equal to the population proportion.

b). For large samples, the possible sample proportions have approximately a normal distribution.

c). Hence, a rule of thumb for using a normal distribution to approximate of all possible sample proportions is that both np and n(1-p) are 5 or greater.

Step by step solution

01

Part (a) Step 1: Given Information

A symmetric probability distribution about the mean indicates that data close to the mean occur more frequently than those further away.

02

Part (a) Step 2: Explanation

A population proportion is a good characteristic of the population.

Hence, the mean of sample proportions is equal to the population proportion.

03

Part (b) Step 1: Given Information

A symmetric probability distribution about the mean indicates that data close to the mean occur more frequently than those further away.

04

Part (b) Step 2: Explanation

The normal distribution is the statistic's probability distribution.

Hence, for large samples, the possible sample proportions have approximately a normal distribution.

05

Part (c) Step 1: Given Information

A symmetric probability distribution about the mean, indicates that data close to the mean occur more frequently than those further away.

06

Part (c) Step 2: Explanation

The maximum value plus two standard deviations and the minimum value minus two standard deviations are the maximum and minimum values, respectively, in a normal distribution.

Hence, a rule of thumb for using a normal distribution to approximate of all possible sample proportions is that both np and n(1-p) are 5 or greater.

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Most popular questions from this chapter

Suppose that you can make reasonably good educated guesses, p^1gand p^2g, for the observed values of p^1and p^2.

a. Use your result from Exercise 11.132to show that a (1-α)-level confidence interval for the difference between two population proportions that has an approximate margin of error of Ecan be obtained by choosing

n1=n2=p^1g1-p^1g+p^2g1-p^2gza/2E2

rounded up to the nearest whole number. Note: If you know likely ranges instead of exact educated guesses for the observed values of the two sample proportions, use the values in the ranges closest to 0.5as the educated guesses.

b. Explain why the formula in part (a) yields smaller (or at worst the same) sample sizes than the formula in Exercise 11.133.

c. When reasonably good educated guesses for the observed values of p^1and p^2can be made, explain why choosing the sample sizes by using the formula in part (a) is preferable to choosing them by using the formula in Exercise 11.133.

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a. At the 1%significance level, do the data provide sufficient evidence to conclude that women who take folic acid are at lesser risk of having children with major birth defects?

b. Is this study a designed experiment or an observational study? Explain your answer.

c. In view of your answers to parts (a) and (b), could you reasonably conclude that taking folic acid causes a reduction in major birth defects? Explain your answer.

We have given a likely range for the observed value of a sample proportionp^

0.2orless

a. Based on the given range, identify the educated guess that should be used for the observed value of p^to calculate the required sample size for a prescribed confidence level and margin of error.

b. Identify the observed values of the sample proportion that will yield a larger margin of error than the one specified if the educated guess is used for the sample-size computation.

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0.00361±1.645·(0.00361)(0.99639)/1109,

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