A sample of 200 observations is taken.The mean is 31.7 and the standard deviation is 1.8.Form a 90 percent confidence interval for the population mean.
A)[31.54 31.86]
B)[28.74 34.66]
C)[28.53 34.87]
D)[31.49 31.91]

Question

Quizplus · Accepted Answer

We can use the formula: 
CI = x̄ ± Z* (σ/√n)
where x̄ is the sample mean, σ is the population standard deviation, n is the sample size, and Z* is the Z-score for the desired confidence level.

For a 90% confidence level, the Z-score is 1.645 (from a standard normal distribution table or calculator).

Plugging in the given values, we get: 
CI = 31.7 ± 1.645 * (1.8/√200) 
CI = 31.7 ± 0.203
CI = [31.497, 31.903]

Rounding to two decimal places gives us the answer: [31.49, 31.91], which is choice (D).

A Sample of 200 Observations Is Taken