Question

QUESTION 7

From a random sample of 97 male students at Hope College, 12 were left-handed.

Determine a 99% confidence interval for the proportion of all male students at Hope College that are

left-handed.

Example: (0.4125,0.6255) - NOTE: This is not the correct answer.

Report your answer to 4 decimal places.

Answer 1

99% Confidence interval: (0.0375,0.2099)

Explanation:

We are given the following in the question:

Sample size, n = 97

Number of left handed, x = 12

`\hat{p} = (x)/(n) = (12)/(97) = 0.1237`

99% Confidence interval:

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

`z_(critical)\text{ at}~\alpha_(0.01) = 2.58`

Putting the values, we get:

`0.1237\pm 2.58(\sqrt{(0.1237(1-0.1237))/(97)}) = 0.1237\pm 0.0862\\\\=(0.0375,0.2099)`

The required confidence interval is (0.0375,0.2099).