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

Answer:

99% Confidence interval:  (0.0375,0.2099)                                  

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 97

Number of left handed, x = 12

$\hat{p} = \dfrac{x}{n} = \dfrac{12}{97} = 0.1237$

99% Confidence interval:

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

$z_{critical}\text{ at}~\alpha_{0.01} = 2.58$

Putting the values, we get:

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

The required confidence interval is (0.0375,0.2099).