Question

A manufacturer of smartphones is interested in designing a new phone around the way a typical customer would use it. One of the most important characteristics for any smartphone is battery life since every activity on a smartphone draws power from the battery in some way. This is especially true for those who use their phones heavily for texting, social media, gaming, etc.

In a marketing research survey, the manufacturer asked a random sample of 25 smartphone owners who consider themselves "heavy users" to run an app on their phone that would record the time the phone is used for various activities (but, for privacy reasons, not record what that activity was).

The company decides to first examine the total minutes used in all activities. The sample mean number of minutes of total use from the 25 users was 117.5, with a standard deviation of 21.6 minutes. Find the upper bound of a 90% confidence interval for the true mean total time that smartphones are used by the population of "heavy users" to one decimal place. Take all calculations toward the answer to three (3) decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 117.5

Population standard deviation =    = 21.6

Sample size = n = 25

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645}

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

= 1.645 * ( 21.6 /  25 )

= 7.106

At Upper bound a 90% confidence interval estimate of the population mean is,

+ E

117.5 + 7.106

124.606

The upper bound of a 90% confidence interval for the true mean total time that smartphones are used :  124.606