Question

Eating Out Vegetarian. Refer to the study on ordering vegetarian considered in Examples 11.8-11.10.

a. Obtain the margin of error for the estimate of the difference between the proportions of men and women who sometimes order veg by taking half the length of the confidence interval found in Example $11.10$on page 473. Interpret your answer in words.

b. Obtain the margin of error for the estimate of the difference between the proportions of men and women who sometimes order veg by applying Exercise 11.132.

Short answer

(a) The margin of error is$0.049$

(b) The estimate of the difference in male and female proportions has a margin of error of $0.049$.

Step-by-step solution

Part (a) Step 1: Given information

Given in the question that, Eating Out Vegetarian. Refer to the study on ordering vegetarian considered in Examples 11.8-11.10.

we need to obtain the margin of error for the estimate of the difference between the proportions of men and women who sometimes order veg by taking half the length of the confidence interval found in Example 11.10 on page 473.

Part(a) Step 2: Explanation

The given value is $p^{\wedge }1=0.369$and $p^{\wedge }2=0.449$

The formula for $E$is given by,

Where $n1=n2=n$

The margin of error is defined as the half-length of the confidence interval.

Calculated the margin of error

localid="1651484628854" $$\begin{gathered} \left(E\right)=-0.031-(-0.129)2 \\ =0.0982 \\ =0.049 \end{gathered}$$

Thus, the margin of error is $0.049$

Part (b) Step 1: Given information

Given in the question that, Refer to the study on ordering vegetarian considered in Examples 11.8-11.10.

We need to obtain the margin of error for the estimate of the difference between the proportions of men and women who sometimes order veg by applying Exercise 11.132.

Part(b) Step 2: Explanation

The given value is $p^{\wedge }1=0.369$and$p^{\wedge }2=0.449.$

The margin of error is

$E=za2p^{\wedge }1\left(1-p^{\wedge }1\right)n1+p2\left(1-p^{\wedge }2\right)n2$

Calculated the margin of error

localid="1651484648579" $$\begin{gathered} E=za2p^{\wedge }1\left(1-p^{\wedge }1\right)n1+p2\left(1-p^{\wedge }2\right)n2 \\ =1.645(0.369(1-0.369)747+0.449(1-0.449\left)434\right) \\ =1.645(0.0297) \\ =0.049 \end{gathered}$$

As a result, the error margin is $0.049$.

As a result, the estimate of the difference in male and female proportions has a margin of error of $0.049$.