Question

35.

According to a poll taken in a certain​ country, when adults were asked whether they were​ thriving, struggling, or​ suffering,

302302

out of

496496

said they were struggling. a. What is the value of

ModifyingAbove p with caretp​,

the sample proportion that say they are​ struggling?

b. Check the conditions to determine whether you can apply the CLT to find a confidence interval.

c. Find a​ 95% confidence interval for the population proportion that say they are struggling.

a. The value of

ModifyingAbove p with caretp​,

the sample proportion that say they are​ struggling, is

nothing.

​(Round to three decimal places as​ needed.)

b. Check the conditions to determine whether you can apply the CLT to find a confidence interval.

The Random and Independent condition

can

reasonably be assumed to hold.The Large Sample condition

holds.

The Big Population condition

holds.

c. The​ 95% confidence interval is

left parenthesis nothing comma nothing right parenthesis,.

​(Round to three decimal places as​ needed.)

Answer 1

a.

302 PE06 = 0.609

b. As n is large and np>10 and nq>10

We can use normal approximation

c. z value for 95% is 1.96 as P(-1.96<z<1.96)=0.95

So Margin of Error is

E = z*= 1.96 + 0.609 * 0,391 – 0.013 n 496

Hence CI is $CI=p\pm E=0.609\pm 0.043=(0.566,0.652)$