A sample of 100 items has a population standard deviation of 5.1 and a mean of 21.6.Construct a 95 percent confidence interval for .
A)[11.60 31.60]
B)[21.16 22.04]
C)[20.60 22.60]
D)[20.76 22.43]

Question

A sample of 100 items has a population standard deviation of 5.1 and a mean of 21.6.Construct a 95 percent confidence interval for  .
A)[11.60 31.60] 
B)[21.16 22.04] 
C)[20.60 22.60] 
D)[20.76 22.43]

Quizplus · Accepted Answer

Use the formula for a confidence interval:
CI = X ± z*(σ/√n), where X is the sample mean, σ is the population standard deviation, n is the sample size, and z is the z-score corresponding to the desired confidence level.

We are given X = 21.6, σ = 5.1, and n = 100. For a 95% confidence level, the z-score is 1.96 (look in a z-table or use a calculator).

Plugging in the values:
CI = 21.6 ± 1.96*(5.1/√100)
CI = 21.6 ± 1.00
CI = (20.60, 22.60)

Therefore, the best choice is C, which matches the calculated confidence interval.

A Sample of 100 Items Has a Population Standard Deviation