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Chapter 10: Q. 22 (page 669)

A random sample of size nwill be selected from a population, and the proportion of those in the sample who have a Facebook page will be calculated. How would the margin of error for a 95%confidence interval be affected if the sample size were increased from 50to 200?

(a) It remains the same.

(b) It is multiplied by 2.

(c) It is multiplied by 4.

(d) It is divided by 2.

(e) It is divided by 4.

Short Answer

Expert verified

Step 1: Given information

Step by step solution

01

Given information

We are given that in random sample of size n ,confidence interval of 95%

From given information we need to find that what will be change in margin of error if sample is increased from 50to 200.

02

Explanation

Confidence level is a range of values so defined that there is a specified probability that the value of a parameter lies within it.

Formula of confidence level is

X¯±Zασ/2n

Where

X¯= Mean

= Confidence coefficient

= Confidence level

= Standard deviation

= sample space

The value after the symbol is known as the margin of error.

We need to find change in margin of error(Let it be )

For confidence intervalwe have

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Most popular questions from this chapter

Young adults living at home A surprising number of young adults (ages 19

to 25) still live in their parents’ homes. The National Institutes of Health surveyed

independent random samples of 2253men and 2629women in this age group. The survey found that 986 of the men and 923 of the women lived with their parents.

a. Construct and interpret a 99%confidence interval for the difference in the true

proportions of men and women aged 19-25who live in their parents’ homes.

b. Does your interval from part (a) give convincing evidence of a difference between the population proportions? Justify your answer.

Final grades for a class are approximately Normally distributed with a mean of 76and a standard deviation of 8. A professor says that the top10%of the class will receive an A, the next20%a B, the next 40%a C, the next 20%a D, and the bottom 10%an F. What is the approximate maximum grade a student could attain and still receive an F for the course?

a.70b.69.27c.65.75d.62.84e.57

Children make choices Refer to Exercise 15.

a. Explain why the sample results give some evidence for the alternative hypothesis.

b. Calculate the standardized test statistic and P-value.

c. What conclusion would you make?

The following dot plots show the average high temperatures (in degrees Celsius) for a sample of tourist cities from around the world. Both the January and July average high temperatures are shown. What is one statement that can be made with certainty from an Page Number: 704 analysis of the graphical display?

a. Every city has a larger average high temperature in July than in January.

b. The distribution of temperatures in July is skewed right, while the distribution of temperatures in January is skewed left.

c. The median average high temperature for January is higher than the median average high temperature for July.

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e. There is more variability in average high temperatures in January than in July

The correlation between the heights of fathers and the heights of their grownup sons, both measured in inches, isr=0.52. If fathers’ heights were measured in feet instead, the correlation between heights of fathers and heights of sons would be

a. much smaller than 0.52.

b. slightly smaller than 0.52.

c. unchanged; equal to 0.52.

d. slightly larger than 0.52.

e. much larger than 0.52.
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