Answer to Question #254230 in Statistics and Probability for Taryn

Question

Suppose that a random sample of 25 mining caps was tested from a population of 3000 mining caps and 20 exploded properly. Give the lower limit of a 80% confidence interval for the proportion of mining caps that will explode properly.

Answer 1

Sample size (n) = 25

Sample proportion (p) = 20 / 25 = 0.8

Confidence interval = 80%

z value at 80% confidence interval = 1.28

Formula to calculate lower limit of a 80% confidence interval for the proportion of mining caps is as follows:

$=p-Z_\frac{\alpha}{2}\sqrt{\frac{p\times(1-p)}{n}}$

$=0.8-1.28\sqrt{\frac{0.8\times(1-0.8)}{25}}$

$=0.8-0.1024 =0.6976$