Question

Which sample size will produce the widest 95% confidence interval, given a sample proportion of 0.5?A.80B.60C.70D.50

Answer 1

Daniel, this is the solution to the problem:

Let's calculate the confidence interval for a sample of 80, as follows:

Z = 1.96 for 95% confidence, therefore:

C.I = (0.5 +/- 1.96 √(0.5 (1 - 0.5)/80)

C.I = 0.5 +/- 0.11

C. I = (0.39, 0.61)

Now, let's do the same calculations for a sample size of 50, this way:

C.I. = (0.5 +/- 1.96 √0.5 (1 - 0.5)/50)

C.I = 0.5 +/- 0.139

C.I = (0.361, 0.639)

Therefore, for a sample size of 80, the wide is 0.22 (0.61 -0.39) and for a sample size of 50, the wide is 0.278 (0.639 - 0.361)

For sample sizes of 60 and 70, the results would be higher than 0.22 but lower than 0.278.

The correct answer is D. 50