# A manufacturer of smartphones

A manufacturer of smartphones is interested in designing a newphone around the way a typical customer would use it. One of themost important characteristics for any smartphone is battery lifesince every activity on a smartphone draws power from the batteryin some way. This is especially true for those who use their phonesheavily for texting, social media, gaming, etc.

In a marketing research survey, the manufacturer asked a randomsample of 25 smartphone owners who consider themselves “heavyusers” to run an app on their phone that would record the time thephone is used for various activities (but, for privacy reasons, notrecord what that activity was).

The company decides to first examine the total minutes used inall activities. The sample mean number of minutes of total use fromthe 25 users was 122.5, with a standard deviation of 20.6 minutes.Find the upper bound of a 90% confidence intervalfor the true mean total time that smartphones are used by thepopulation of “heavy users” to one decimal place. Take allcalculations toward the answer to three (3) decimalplaces.

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= 0.05t/2,df= t0.05,24 = 1.71

t/2,df = 1.71

Margin of error = E = t/2,df* (s /$\sqrt$n)

= 1.71 * (20.6 / $\sqrt$25)

Margin of error = E = 7.049

The 90% confidence interval estimate of the population meanis,

– E < <  +E

122.5 -7.049 < < 122.5+ 7.049

115.451< < 129.549

(115.451,129.549)

ANSWER = Upper bound is = 129.549

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