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)± 0.0288
B)± 0.0105
C)± 0.0207
D)± 0.0196

Question

Quizplus · Accepted Answer

We can use the formula for the margin of error in a proportion confidence interval:

Margin of Error = Z* * sqrt((p * (1-p))/n)

where Z* is the critical value for the desired confidence level (95% in this case), p is the sample proportion, and n is the sample size.

Substituting in the values given:

Z* = 1.96 (from standard normal table)
p = 81/810 = 0.1
n = 810

Margin of Error = 1.96 * sqrt((0.1 * (1-0.1))/810) ≈ 0.0207

So the width of the 95% confidence interval is twice the margin of error, or approximately ±0.0207. Therefore, the best choice is C.

In a Random Sample of 810 Women Employees,it Is Found