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Chapter 11: Q.7 (page 480)

Suppose that you are using independent samples to compare two population proportions.

Fill in the blanks.

a. The mean of all possible differences between the two sample proportions equals the

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

Short Answer

Expert verified

a). The mean of all possible differences between the two sample proportions equals the difference in population proportion.

b). For a huge sample, the differences between the two sample proportions have approximately a normal distribution.

Step by step solution

01

Part (a) Step 1: Given Information

A population proportion is a percentage of the total population that shares a particular trait.

02

Part (a) Step 2: Explanation

When comparing two population proportions, independent samples are used.

A population proportion is a good characteristic of the population.

The mean of all possible differences between the two sample proportions equals the difference in 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

When comparing two population proportions, independent samples are used.

The probability distribution of a statistic is known as its normal distribution.

For a huge sample, the differences between the two sample proportions have approximately a normal distribution.

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Most popular questions from this chapter

Christmas Presents. The Arizona Republic conducted a telephone poll of 758Arizona adults who celebrate Christmas. The question asked was, "In your family, do you open presents on Christmas Eve or Christmas Day?" Of those surveyed, 394said they wait until Christmas Day.

a. Determine and interpret the sample proportion.

b. At the 5%significance level, do the data provide sufficient evidence to conclude that a majority (more than 50%) of Arizona families who celebrate Christmas wait until Christmas Day to open their presents?

A poll conducted by Gallup in December 2013asked a sample of American adults whether they approved of the way President Obama was doing his job; 42%said yes, with a margin of error of plus or minus 3percentage points. During that same time period, Quinnipiac University asked the same question of a sample of American adults; 38%said yes, with a margin of error of plus or minus2 percentage points. Can the conclusions of both polls be correct? Explain your answer.

Margin of error=0.01

Confidence level=90%

Educated guess=0.9

(a) 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 0.5that of the educated guess.

(b). Compare your answer to the corresponding one and explain the reason for the difference, if any.

Prerequisites to this exercise are Exercises . Why do your graphs in parts (c) of those exercises illustrate the impact of increasing sample size on sampling error? Explain your answer.

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.
See all solutions

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