In a random sample of 810 women employees, it is found that 81 would prefer working for a female boss. The width of the 95 percent confidence interval for the proportion of women who prefer a female boss is:
A)± .0288
B)± .0105
C)± .0207
D)± .0196

Question

Quizplus · Accepted Answer

To calculate the width of the confidence interval for a proportion, we use the formula:

width = 2 * z * sqrt(p̂(1-p̂)/n)

where z is the z-score for the desired confidence level (1.96 for 95% confidence), p̂ is the sample proportion (81/810 = 0.1), and n is the sample size (810).

Plugging in these values, we get:

width = 2 * 1.96 * sqrt(0.1(1-0.1)/810) ≈ 0.0207

Therefore, the width of the 95% confidence interval for the proportion of women who prefer a female boss is ±0.0207. The closest answer choice is C.

In a Random Sample of 810 Women Employees, It Is