Mathematics, 12.08.2020 04:01 BrookLPrescott287

The research group asked the following question of individuals who earned in excess of $100,000 per year and those who earned less than $100,000 per year: "Do you believe that it is morally wrong for unwed women to have children?" Of the individuals who earned in excess of $100,000 per year, said yes; of the individuals who earned less than $100,000 per year, said yes. Construct a 95% confidence interval to determine if there is a difference in the proportion of individuals who believe it is morally wrong for unwed women to have children.

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Answer from: naddiachoudry9970

Complete Question

The complete question is shown on the first uploaded image

The lower bound is 0.0234

The upper bound is 0.100

So from the value obtained the solution to the question are

1 Does not include

2 sufficient

3 not different

Step-by-step explanation:

From the question we are told that

The sample size of individuals who earned in excess of $100,000 per year is n_ 1 = 1205

The number of individuals who earned in excess of $100,000 per year that said yes is

w = 712

The sample size individuals who earned less than $100,000 per year is n_2 = 1310

The number of individuals who earned less than $100,000 per year that said yes is

v= 693

The sample proportion of individuals who earned in excess of $100,000 per year that said yes is

$\r p _ 1 = \frac{w}{n_1 }$

substituting values

$\r p _ 1 = \frac{712}{1205}$

$\r p _ 1 =0.5909$

The sample proportion of individuals who earned less than $100,000 per year that said yes is

$\r p _ 1 = \frac{v}{n_2 }$

substituting values

$\r p _ 1 = \frac{693 }{1310}$

$\r p _ 1 = 0.529$

Given that the confidence level is 95% then the level of significance is mathematically represented as

$\alpha = 1 -0.95$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table the value is $Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is

$E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{ \r p _1 (1- \r p_1 )}{n_1} + \frac{ \r p _2 (1- \r p_2 )}{n_2} } }$

substituting values

$E = 1.96 * \sqrt{ \frac{ 0.5909 (1- 0.5909 )}{1205} + \frac{ 0.592 (1- 0.6592 )}{1310} } }$

E =0.03846

Generally the 95% confidence interval is

$(\r p_1 - \r p_2) - E < p_1 - p_2$

substituting values

(0.5909 - 0.529 ) - 0.03846 < p_1 - p_2 < (0.5909 - 0.529 ) + 0.03846

0.02344 < p_1 - p_2 < 0.10036

The lower bound is 0.0234

The upper bound is 0.100

So from the value obtained the solution to the question are

1 Does not include

2 sufficient

3 not different

The research group asked the following question of individuals who earned in excess of $100,000 per

Answer from: Quest

b is the answer that makes most sense

step-by-step explanation:

Answer from: Quest

y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x y

0 0

1 -3

3 -9

-2 6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.

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