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

Answer:

The 90% confidence interval is (0.383,0.497)    

Step-by-step 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

$\hat{p} = \dfrac{x}{n} = \dfrac{88}{200} = 0.44$

90% Confidence interval:

$\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$z_{critical}\text{ at}~\alpha_{0.10} = \pm 1.64$

Putting the values, we get:

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

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%