Question

In a study, a random sample of 2625 US adults were asked whether they agree or disagree that there is "only one true love for each person." The response and gender of the participants is shown in Table 1.


Male Female Total

Agree 372 363 735

Disagree 807 1005 1812

Don't know 34 44 78

Total 1213 1412 2625


Table 1 Is there only one true love for each person?


(a) Use the information in the table to construct a confidence interval for the difference in the proportion who agree, between males and females, using the fact that the standard error for the difference is .


Round your answers to three decimal places.


The 95% confidence interval is

to

.


(b) Is it plausible that there is no difference between males and females in the proportion who agree that each person has only one true love?

Answer 1

Using the information given, it is found that:

a.

The standard error for the difference is of 0.0176.

The 95% confidence interval is 0.0151 to 0.0841.

b.

Since 0 is not part of the confidence interval, it is not plausible that there is no difference between males and females in the proportion who agree that each person has only one true love.

What is the distribution of differences for the proportion of males and females?

For males, we have that:

$n = 1213, p_M = \frac{372}{1213} = 0.3067, s_M = \sqrt{\frac{0.3067(0.6933)}{1213}} = 0.01324$

For females, we have that:

$n = 1412, p_F = \frac{363}{1412} = 0.2571, s_F = \sqrt{\frac{0.2571(0.7429)}{1412}} = 0.01163$

The distribution of differences has mean and standard error given by:

$p = p_M - p_F = 0.3067 - 0.2571 = 0.0496$

$s = \sqrt{s_M^2 + s_F^2} = \sqrt{0.01324^2 + 0.01163^2} = 0.0176$

What is the confidence interval?

It is given by:

$p \pm zs$

z is the critical value, which considering that there is a 95% confidence level, it is of z = 1.96.

Then:

$p - zs = 0.0496 - 1.96(0.0176) = 0.0151$

$p + zs = 0.0496 + 1.96(0.0176) = 0.0841$

The 95% confidence interval is 0.0151 to 0.0841.

Item b:

Since 0 is not part of the confidence interval, it is not plausible that there is no difference between males and females in the proportion who agree that each person has only one true love.

More can be learned about confidence intervals at https://brainly.com/question/16162795