Question

An inexperienced on-line instructor would like to estimate the mean time that it takes her students to complete one of her tests. She takes a random sample of 30 test times and finds that the mean in the sample is 36 minutes with a standard deviation in the sample of 3 minutes. Which of the following would be the appropriate calculation for constructing a 98% confidence interval to estimate the mean test time for all of her students? a. 34.726 <u <37.274 b. 34.652 < <37.348 OC 28.769 <u <31.231 Od. 28.614<p < 43.386

Answer 1

Answer:

b. 34.652 < µ < 37.348

Solution:

Confidence interval for Population mean is given as below:

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

From given data, we have

Xbar = 36

S = 3

n = 30

df = n – 1 = 29

Confidence level = 98%

Critical t value = 2.4620

(by using t-table)

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

Confidence interval = 36 ± 2.4620*3/sqrt(30)

Confidence interval = 36 ± 1.348505

Lower limit = 36 ± 1.348505 = 34.652

Upper limit = 36 ± 1.348505 = 37.348