Question

Suppose scores exams in statistics with an unknown population mean and a sample standard deviation of 2 points. A random sample of 16 scores is taken and gives a sample mean. (sample mean score) of 8. Find the confidence interval estimate for the population mean test score ( the mean score of all tests).

Find a 90% confidence interval for the true (population) mean of statistics test scores.

Answer 1

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± Z*σ/sqrt(n)

From given data, we have

Xbar = 8

σ = 2

n = 16

Confidence level = 90%

Critical Z value = 1.6449

(by using z-table)

Confidence interval = Xbar ± Z*σ/sqrt(n)

Confidence interval = 8 ± 1.6449*2/sqrt(16)

Confidence interval = 8 ± 1.6449*0.5000

Confidence interval = 8 ± 0.8224

Lower limit = 8 - 0.8224 = 7.18

Upper limit = 8 + 0.8224 = 8.82

Confidence interval = (7.18, 8.82)