Chapter 8: Q.67 (page 481)

Construct a $95 %$ confidence interval for the population proportion of households where the women make the majority of the purchasing decisions. State the confidence interval, sketch the graph and calculate the error bound.

Short Answer

Expert verified

The confidence interval: $C I : (0.532, 0.668)$

Margin of error $= 0.0679$

Step by step solution

Given Information

A $95 %$ confidence interval for the population proportion of households.

Explanation

Here we need to find the margin of errors,

That are,

$Margin Of Error = [Z_{\frac{α}{2}} \times \sqrt{\frac{p^{'} (1 - p^{'})}{n}}]$

$= [Z_{\frac{0.05}{2}} \times \sqrt{\frac{\frac{120}{200} (1 - \frac{120}{200})}{200}}]$

$= [1.96 \times 0.03464]$

$= 0.0679$

Now we need to find the confidence interval

$Confidence Interval = [p^{'} \pm Z_{\frac{a}{2}} \times \sqrt{\frac{p (1 - p)}{n}}]$

$= [\frac{120}{200} \pm Z \frac{0.05}{2} \times \sqrt{\frac{\frac{120}{200} (1 - \frac{120}{200})}{200}}]$

$= [\frac{120}{200} \pm 1.96 \times 0.03464]$

$= [0.532, 0.668]$

The confidence interval is $C I : (0.532, 0.668)$ .

The graph:

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Construct a $95 %$ confidence interval for the population proportion of households where the women make the majority of the purchasing decisions. State the confidence interval, sketch the graph and calculate the error bound.

Short Answer

Step by step solution

Given Information

Explanation

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Construct a 95% confidence interval for the population proportion of households where the women make the majority of the purchasing decisions. State the confidence interval, sketch the graph and calculate the error bound.

Short Answer

Step by step solution

Given Information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Geometry

Applied Mathematics

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Construct a $95 %$ confidence interval for the population proportion of households where the women make the majority of the purchasing decisions. State the confidence interval, sketch the graph and calculate the error bound.