Question

Nine students were randomly selected from a population of 1000 students and they were given a math test. Test results are: 95  90   89   85   76 73   92   90  72     What is the 84% confidence interval for the population mean score on the math tests?

a) Do you need any assumptions? If yes, make the assumption.

b) Name the interval

c) 84% CI is

Answer 1

Part a

Yes, we assume that the population is normally distributed.

Part b

t-confidence interval

Part c

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 84.66666667

S = 8.717797887

n = 9

df = n – 1 = 8

Confidence level = 84%

Critical t value = 1.5489

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 84.66666667 ± 1.5489*8.717797887 /sqrt(9)

Confidence interval = 84.66666667 ± 4.5010

Lower limit = 84.66666667 - 4.5010 = 80.1657

Upper limit = 84.66666667 + 4.5010 = 89.1676

Confidence interval = (80.1657, 89.1676)