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 122.5, with a standard deviation of 20.6 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 = = 122.5

sample standard deviation = s = 20.6

sample size = n = 25

Degrees of freedom = df = n - 1 = 25 - 1 = 24

At 90% confidence level

= 1-0.90% =1-0.9 =0.10

/2 =0.10/ 2= 0.05

t/2,df = t_{0.05,24 = 1.71}

t _/2,df = 1.71

Margin of error = E = t_/2,df * (s /n)

= 1.71 * (20.6 / 25)

Margin of error = E = 7.049

The 90% confidence interval estimate of the population mean is,

- E < <  + E

122.5 -7.049 < < 122.5+ 7.049

115.451< < 129.549

(115.451,129.549)

ANSWER = Upper bound is = 129.549