Question

Faculty members at Lowell Place High School want to determine whether there are enough students to have a Valentine's Day Formal. Eighty-eight of the 200 students said they would attend the Valentine's Day Formal. Construct and interpret a 90% confidence interval for p.

Answer 1

The 90% confidence interval is (0.383,0.497)

Explanation:

We are given the following in the question:

Sample size, n = 200

Number of children that would attend Valentine's Day Forma, x = 88

`\hat{p} = (x)/(n) = (88)/(200) = 0.44`

90% Confidence interval:

`\hat{p}\pm z_(stat)\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}`

`z_(critical)\text{ at}~\alpha_(0.10) = \pm 1.64`

Putting the values, we get:

`0.44\pm 1.64(\sqrt{(0.44(1-0.44))/(200)}) = 0.44\pm 0.057\\\\=(0.383,0.497)`

Interpretation:

The 90% confidence interval is (0.383,0.497). We are 90% confident that the proportion of children attending Valentine's Day Formal is between 38.3% and 49.7%