Question

A national survey of 2500 adukt citizens of a nation found that 21 % dreaded Valentine's Day. The margin of error for the survey was 5.4 percentage points with 90% confidence. explain what this means.

which statement below is the best explanation?

a. there is 84.6% to 95.4% confidence that 25% of the adult citizens of the nation dreaded Valentine's Day
b. in 90% of samples of adult citizens of the nation, the proportion that dreaded Valentine's Day is between 0.196 and 0.304.
c. there is 90% confidence that the proportion of the adult citizens of the nation that dreaded Valentine's Day is between 0.196 and 0.304.
d. there is 90% confidence that 25% of the adult citizens of the nation dreaded Valentines Day.

Answer 1

The correct option is C

Explanation:

From the question we are told that

The sample size is
`n = 2500`

The sample proportion is
`\r p = 0.21`

The margin of error is
`E = 0.054`

The 90% confidence interval is mathematically represented

`\r p - E < p < \r p + E`

=>
`0.21 - 0.054 < p < 0.21 + 0.054`

=>
`0.156< p < 0.264`