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, 347, 274, 316, 286, 341, 347, 291 Assume that it is reasonable to believe that the population is approximately normal and the population standard deviation is 70. What is the upper bound of the 95% confidence interval for the battery life for all e-readers of this type? Round your answer to one decimal places (for example: 319.4). Write only a number as your answer. Do not write any units.

Answer 1

Solution :

Given that,

Sample size = n =

Point estimate = sample mean = = / n

= 287+ 311+262+392+313+347+274+316+286+341+347+291 / 12

​ = 313.9

Population standard deviation = = 70

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

Z= Z _0.05 = 1.645

Margin of error = E = Z_/2* ( /n)

= 1.645 * ( 70 / 12 )

= 33.2

At 95% upper confidence interval estimate of the population mean is,

+ E

313.9 + 33.2 = 347.1

upper bound = 347.1