A research firm wants to compute an interval estimate with 90% confidence for the mean time to complete an employment test. Assuming a population standard deviation of three hours,what is the required sample size if the error should be less than a half hour?
A)196
B)98
C)10
D)16

Question

Quizplus · Accepted Answer

The formula for the margin of error is: Margin of error = z* (σ/√n) where z* is the z-value corresponding to the desired level of confidence (in this case 1.645 for 90% confidence), σ is the population standard deviation, and n is the sample size. We want the margin of error to be less than a half hour, or 0.5. So we can set up the following inequality: z* (σ/√n) < 0.5 Plugging in the given values, we get: 1.645 (3/√n) < 0.5 Solving for n: n > (1.645*3/0.5)^2 n > 97.9921 We need a sample size greater than 97.9921 in order to have a margin of error less than 0.5. Since we can't have a fraction of a person, we round up to the next integer to get our final answer: n = 98 Therefore, the required sample size is 98. Answer is B.

A Research Firm Wants to Compute an Interval Estimate with 90