In a recent research poll, 83.4% of 500 randomly selected men in the U. S. knew the name of our current vice president. When 500 randomly selected women in the U. S. were asked, 79% knew the vice president’s name.

(a) Construct and interpret a 95% confidence interval for the true difference in the proportion of U. S. men and the proportion of U. S. women who know the name of our current vice president.

(b) Based on this confidence interval, is there convincing evidence that the true proportion of men who know the name of the current vice president is different than the true proportion of women that know the name the current vice president? Explain.

a)

The 95% confidence interval for the true difference of proportions is given by (-0.00435;0.0924)

b) For this case since the confidence interval contians the value 0 we can't conclude that the true proportion of men who know the name of the current vice president is different than the true proportion of women that know the name the current vice president at 5% of significance

Step-by-step explanation:

Part a

Since our interval is at 95% of confidence, our significance level would be given by and . And the critical value would be given by:

The confidence interval for the difference of proportions is given by the following formula:  

Replacing the info given we got:

The 95% confidence interval for the true difference of proportions is given by (-0.00435;0.0924)

Part b

For this case since the confidence interval contians the value 0 we can't conclude that the true proportion of men who know the name of the current vice president is different than the true proportion of women that know the name the current vice president at 5% of significance

i can't see the picture : /

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.