Question

A poll reported that only 344 out of a total of 1507 adults in a particular region said they had a​ "great deal of​ confidence" or​ "quite a lot of​ confidence" in the public school system. This was down 5 percentage points from the previous year. Assume the conditions for using the CLT are met. Complete parts​ (a) through​ (d) below.

a. Find a 95​% confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public​ schools, and interpret this interval.

The 95% confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public schools is Answer (_____ and _____)

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

We are Answer ____% confident that the population proportion of adults having a great deal or quite a lot of confidence in the public schools is between Answer (____ and ____)

B.. Find a 90​% confidence interval and interpret it.The 90​% confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public schools is

Answer (___, and ____) ​(Round to three decimal places as​ needed.)

Interpret this interval. Select the correct choice below and fill in the answer boxes to complete your choice.

​(Type integers or decimals rounded to three decimal places as​ needed.)

c. Find the width of each interval by subtracting the lower proportion from the upper​ proportion, and state which interval is wider. The width of the 95​% confidence interval is

Answer _____ and the width of the 90​% confidence interval is Answer _____ . The is wider.  (Round to three decimal places as​ needed.)

d. How would a 95% interval compare with the others in​ width? Answer _____ (A,B,C or D)

A. A 95​% interval would be narrower than the 99% confidence interval but wider than the 90​% confidence because intervals get wider with increasing confidence level.Your answer is correct.

B.A 95​% interval would be wider than the 99% confidence interval but narrower than the 90​% confidence because intervals get narrower with increasing confidence level.

C.A 95% interval would be wider than the 99​% confidence interval but narrower than the 90​% confidence because intervals get wider with increasing confidence level.

D.A 95% interval would be narrower than the 99​% confidence interval but wider than the 90% confidence because intervals get narrower with increasing confidence level.

Answer 1

given data are:-

sample size(n) = 1507

sample proportion () = 344/1507 = 0.2283

a). z critical value for 95% confidence level, both tailed test be:-

The 95% confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public schools is:-

We are 95 % confident that the population proportion of adults having a great deal or quite a lot of confidence in the public schools is between 0.207 and 0.249

b). z critical value for 90% confidence level, both tailed test be:-

The 90% confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public schools is:-

We are 90  % confident that the population proportion of adults having a great deal or quite a lot of confidence in the public schools is between 0.211 and 0.247

c).The width of the 95​% confidence interval is :-

= ( 0.249 -0.0207)

= 0.042

The width of the 90​% confidence interval is :-

= ( 0.247 -0.0211)

= 0.036

the 95 % confidence interval is wider.

d).the correct option is:-

A 95% interval would be narrower than the 99​% confidence interval but wider than the 90% confidence because intervals get narrower with increasing confidence level. (D)

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