Statistics Through Applications
Statistics Through Applications
2nd Edition
ISBN: 9781429219747
Author: Daren S. Starnes, David Moore, Dan Yates
Publisher: Macmillan Higher Education
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Chapter 9, Problem 9.67RE

a)

To determine

To find the 99% confidence interval for p

a)

Expert Solution
Check Mark

Answer to Problem 9.67RE

The 99% confidence interval is, (6690,7400)

Explanation of Solution

Given:

C=confidence level = 0.99

n =1100

  x = 775

Formula:

Confidence interval for population proportion is,

  CI=p^E

Sample proportion:

  p^=xn

Margin of error:

  E=Zc×p^(1p^)n

Calculation:

Sample proportion:

  p^=7751100=0.7045

Z critical value can be found either by using standard normal table or excel formula.

Therefore, level of significance = a = 1-0.99 = 0.01

So, Zc =Za/2 = Z0.01/2

Using excel function, =ABS(NORMSINV(0.01/2))

Zc = 2.58

Therefore, margin of error is,

  E=2.58×0.7045(10.7045)1100=0.0355

99% confidence interval for population proportion,

  p^E=0.70450.0355=0.6690p^+E=0.7045+0.0355=0.7400

We are 99% confident that the true proportion of teenagers that play games online is between 0.6690 and 0.7400

b)

To determine

To explain whether margin of error will be changed for confidence interval of boys and girls.

b)

Expert Solution
Check Mark

Answer to Problem 9.67RE

Margin of error will be smaller.

Explanation of Solution

The margin of error will be depending on the sample size. The sample size for girls and boys separately will be smaller than overall sample. Therefore, the margin of error to be larger for smaller sample.

c)

To determine

To explain real issues that are not explained by margin of error.

c)

Expert Solution
Check Mark

Explanation of Solution

The errors which not included in the margin of error is sampling variability. There are two mainly types of errors. Response bias and non-response bias.

Response bias: In this bias, the responders gives different response than true values.

Non response bias: It occurs when results of not having data for everybody in the sample.

Chapter 9 Solutions

Statistics Through Applications

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