Question

A poll of 1021 U.S. adults split the sample into four age​ groups: ages​ 18-29, 30-49,​ 50-64, and​ 65+. In the youngest age​ group, 60​% said that they thought the U.S. was ready for a woman​ president, as opposed to 37​% who said​ "no, the country was not​ ready" (3% were​ undecided). The sample included 255​18- to​ 29-year olds.

​a) Do you expect the 90% confidence interval for the true proportion of all​ 18- to​ 29-year olds who think the U.S. is ready for a woman president to be wider or narrower than the

90

​%

confidence interval for the true proportion of all U.S.​ adults?

​b) Construct a

90

​%

confidence interval for the true proportion of all​ 18- to​ 29-year olds who believe the U.S. is ready for a woman president.

​a) The

90

​%

confidence interval for the true proportion of​ 18- to​ 29-year olds who think the U.S. is ready for a woman president will be about

▼

twice

equally

four times one-fourth one-half as wide as the 90% confidence interval for the true proportion of all U.S. adults who think this.

​b) The 90% confidence interval is ( % , % )

.​(Round to one decimal place as​ needed.)

Answer 1

Answer :-

Given that,

A poll of 1021 U.S. adults split the sample into four age​ groups: ages​ 18-29, 30-49,​ 50-64, and​ 65+

In the youngest age​ group, 60​% said that they thought the U.S. was ready for a woman​ president, as opposed to 37​% who said​ "no, the country was not​ ready"

(a) Here,we need to find 90% confidence interval for the true proportion of all​ 18- to​ 29-year olds who think the U.S. is ready for a woman president to be wider or narrower than the 90​% confidence interval for the true proportion of all U.S.​ adults.

Then,

The size of 18-29 age gathering is 255. Where as the all out four age gatherings comprises of 1021 which is multiple times bigger than the more youthful gathering. Continuously bigger the example size littler will be room for give and take and smaller will be the spread of the interim. Consequently the 90% certainty interim for the populace extent of 18-29 age gathering will be twice wide as that of the certainty interim for the genuine extent of all the US grown-ups since its example is one fourth bigger here note that we expect roughly equivalent extents.

(b)  Here,we need to find Construct a 90​% confidence interval for the true proportion of all​ 18- to​ 29-year olds who believe the U.S. is ready for a woman president

In the youngest age​ group, 0.60 said that they thought the U.S. was ready for a woman​ president, as opposed to 0.37 who said​ "no, the country was not​ ready"

to know the value of sample proportion we have formula as

sample proportion =

=

  

0.02950 is the sample proportion of the sample

now, need to find 90% confidence interval p can be taken as 1.645 is a standard value.

to know the value we have formula as

  

  

Therefore,

90% confidence interval for the true proportion of all​ 18- to​ 29-year olds who believe the U.S. is ready for a woman president is (0.6485275,0.5514725)

Now we are rounding in 1 decimal place then (0.6,0.5)

where (6%,5%) respectievely.

Thank you