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Get Full Access to Openintro Statistics - 3 Edition - Chapter 6 - Problem 6.4
Get Full Access to Openintro Statistics - 3 Edition - Chapter 6 - Problem 6.4

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# About 25% of young Americans have delayed starting a

ISBN: 9781943450039 86

## Solution for problem 6.4 Chapter 6

OpenIntro Statistics | 3rd Edition

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Problem 6.4

About 25% of young Americans have delayed starting a family due to the continued economic slump. Determine if the following statements are true or false, and explain your reasoning.37 (a) The distribution of sample proportions of young Americans who have delayed starting a family due to the continued economic slump in random samples of size 12 is right skewed. (b) In order for the distribution of sample proportions of young Americans who have delayed starting a family due to the continued economic slump to be approximately normal, we need random samples where the sample size is at least 40. (c) A random sample of 50 young Americans where 20% have delayed starting a family due to the continued economic slump would be considered unusual. (d) A random sample of 150 young Americans where 20% have delayed starting a family due to the continued economic slump would be considered unusual. (e) Tripling the sample size will reduce the standard error of the sample proportion by one-third

Step-by-Step Solution:

Problem 6.4

About 25% of young Americans have delayed starting a family due to the continued economic slump. Determine if the following statements are true or false, and explain your reasoning.

(a) The distribution of sample proportions of young Americans who have delayed starting a family due to the continued economic slump in random samples of size 12 is right skewed.

(b) In order for the distribution of sample proportions of young Americans who have delayed starting a family due to the continued economic slump to be approximately normal, we need random samples where the sample size is at least 40.

(c) A random sample of 50 young Americans where 20% have delayed starting a family due to the continued economic slump would be considered unusual.

(d) A random sample of 150 young Americans where 20% have delayed starting a family due to the continued economic slump would be considered unusual.

(e) Tripling the sample size will reduce the standard error of the sample proportion by one-third

Step by Step Solution

Step 1 of 2

The sampling distribution for , taken from a sample of size n from a population with a true proportion p, is nearly normal when

The sample observations are independent and

We expected to see at least 10 successes and 10 failures in our sample, i.e.  and . This is called the success-failure condition.

If these conditions are met, then the sampling distribution of ˆp is nearly normal with mean p and standard

Given,

Population proportion, p = 25% = 0.25

Step 2 of 2

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