Question

A student has been spending exactly four hours on every assignment she has been assigned this year. She took a random sample of sixteen of her assignments and their word count. She found the average word count in this sample to be 1140 words, with a standard deviation of 397 words. Construct a 95% confidence interval for the mean number of words she writes.

Answer 1

Solution:

Confidence interval for Population mean is given as below:

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

From given data, we have

Xbar = 1140

S = 397

n = 16

df = n – 1 = 15

Confidence level = 95%

Critical t value = 2.1314

(by using t-table)

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

Confidence interval = 1140 ± 2.1314*397/sqrt(16)

Confidence interval = 1140 ± 211.5464

Lower limit = 1140 - 211.5464 = 928.45

Upper limit = 1140 + 211.5464 = 1351.55

Confidence interval = (928.45, 1351.55)