A national survey of 2500 adult citizens of a nation found that 16% dreaded Vale

Question

A national survey of 2500 adult citizens of a nation found that 16% dreaded Valentine's day. The margin of error for the survey was 7.5 percentage points with 90% confidence. Explain what this means.

Which statement below is the best explanation?

a) There is 82.5% to 97.5% confidence that 16% of the adlt citizens of the nation dreaded Valentine's Day.

b) There is 90% confidence that the proportion of the adult citizens of the nation that dreaded Valentines day between 0.085 and 0.235.

c) There is 90% confidence that 16% of the adult ciizens of the nation dreaded valentines day.

d) In 90% of samples of adult citizens of the nation, the proportion that dreaded valentines day is between 0.085 and 0.235

Explanation / Answer

Here we have given that

n= No of adult citizens = 2500

P = proportion that the adult citizens dreaded valentine's day = 0.16

margin of error=E = 7.5

c= condidence level= 0.90

that is

90 % confidence interval for the population proportion shows that we are 90 % confident that the population propotion is falls withiin this interval

that is here

Option B is correct.

There is 90% confidence that the proportion of the adult citizens of the nation that dreaded Valentines day between 0.085 and 0.235.

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