A sample of 225 elements from a population with a standard deviation of 75 is selected. The sample mean is 180. The 95% confidence interval for μ is
A) 105.0 to 225.0
B) 175.0 to 185.0
C) 100.0 to 200.0
D) 170.2 to 189.8

Question

Quizplus · Accepted Answer

The formula for a 95% confidence interval is:

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 critical value from the standard normal distribution corresponding to a 95% level of confidence (which is 1.96).

Plugging in the values given in the problem, we get:

180 ± 1.96*(75/√225)

= 180 ± 1.96*(5)

= 180 ± 9.8

The 95% confidence interval for μ is therefore (180 - 9.8) to (180 + 9.8), or 170.2 to 189.8. Therefore, the best choice is D.

A Sample of 225 Elements from a Population with a Standard