We are to estimate the confidence interval for a population proportion p, based on two samples A and B of sizes 100 and 200, respectively. Both samples have the same standard deviations. Compare the lengths of the 95% confidence interval based on A to the interval based on B. A. The length of the confidence interval based on A is the same as the length of the confidence interval based on B since the standard deviations for both samples are the same.
B. The length of the confidence interval based on A is larger than the length of the confidence interval based on B since SE for the sample A is larger than SE for the sample
C. The length of the confidence interval based on A is larger than the length of the confidence interval based on B since SE for the sample A is less than SE for the sample B.
D. The length of the confidence interval based on A is less than the length of the confidence interval based on B since SE of the sample A is larger than SE of the sample B.
E. The length of the confidence interval based on A is less than the length of the confidence interval based on B since SE of the sample A is less than the size of the sample B.

The option B is True

Step-by-step explanation:

Solution

nA  < nB

Thus

1/√nA > 1/√nB

SD/√nA  > SD/√nB

So,

SE (A) > SE (B)(1)

Zα/2 SE (A) > Zα/2 SE (B)

Now

E (A) > E(B)  this is the margin error

Since SE fro sample A is larger than SE for sample B

We have that,

The length = ZE

Therefore, option B is correct because here, we know that as the sample size increases or goes higher  the length of the confidence interval decreases

In this case, the  sample size is large for B then A.

Thus, the length of confidence interval based on A is larger than the length of confidence interval Based on B Since SE is large For A than B

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.