Question

A simple random sample of 12 e-readers of a certain type had the following minutes of battery life. 287, 311, 262, 392, 313, 316, 280, 316, 286, 333, 329, 291 Assume that it is reasonable to believe that the population is approximately normal and the population standard deviation is 75. What is the upper bound of the 95% confidence interval for the battery life for all e-readers of this type?

Answer 1

Confidence interval for Population mean is given as below:

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

From given data, we have

Xbar = 309.6666667

S = 33.52701308

n = 12

df = n – 1 = 11

Confidence level = 95%

Critical t value = 2.2010

(by using t-table)

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

Confidence interval = 309.6666667 ± 2.2010*33.52701308/sqrt(12)

Confidence interval = 309.6666667 ± 2.2010* 9.678415013

Confidence interval = 309.6666667 ± 21.3020

Lower limit = 309.6666667 - 21.3020 = 288.36

Upper limit = 309.6666667 + 21.3020 = 330.97

Confidence interval = (288.36, 330.97)

Upper bound = 330.97