A researcher collects 25 data points that yield a mean of 8.164 and a standard deviation (based on N - 1) of 2.237.If the researcher is comparing the sample to a population mean of 9.2, what is the 95 percent confidence interval?
A) [6.92, 9.41]
B) [7.24, 9.09]
C) [7.75, 8.58]
D) [7.85, 10.48]

Question

Quizplus · Accepted Answer

To calculate the confidence interval, we use the formula:
CI = X̄ ± t(α/2, n-1) * (s/√n)
where X̄ is the sample mean, t(α/2, n-1) is the t-score for a given level of confidence (in this case 95% and degrees of freedom = n-1 = 24), s is the sample standard deviation, and n is the sample size.

Plugging in the given values:
X̄ = 8.164
s = 2.237
n = 25
t(α/2, n-1) = 2.064 (from t-table for degrees of freedom = 24 and 95% confidence level)

CI = 8.164 ± 2.064 * (2.237/√25) = [7.24, 9.09]

Therefore, the correct choice is B.

A Researcher Collects 25 Data Points That Yield a Mean