Answer:
A sample of 675 office workers would be needed to estimate the proportion of workers who respond to emails within 0.05 hours with 90% confidence.
Explanation:
To determine the sample size needed, we need to use the following formula:
n = (Z^2 * p * q) / E^2
Where:
n is the sample size needed
Z is the Z-score corresponding to the desired level of confidence (in this case, 90% confidence corresponds to a Z-score of 1.645)
p is the estimated proportion of office workers who respond to e-mail within the desired time frame (we don't have an estimate, so we will assume a conservative estimate of 0.5)
q is the complement of p (q = 1 - p)
E is the margin of error we want to achieve (in this case, 0.05)
Plugging in the values, we get:
n = (1.645^2 * 0.5 * 0.5) / 0.05^2
n = 674.52
Rounding up to the nearest whole number, we get a sample size of 675. Therefore, we would need to sample 675 office workers in order to estimate the proportion of workers who respond to e-mails within 0.05 hours with 90% confidence.