Question

(No scribbling/chicken scratch! Please show work)

1. A researcher at the Annenberg School of Communication is interested in studying the use of smartphones among young adults. She wants to know the average amount of time that college students in the United States hold a smartphone in their hand each day. The researcher obtains data for one day from a random sample of 25 college students (who own smartphones). She installs an app that registers whenever the smartphone is being held and the screen is on. The sample mean is 230 minutes, with a standard deviation of 11 minutes.

a) What is the 95% confidence interval for average daily time a smartphone is used among college students?

b) What value of t is used in the confidence interval?

c) What is the standard error?

d) What is the lower bound of the confidence interval and the upper bound of the confidence interval?

Answer 1

Solution :

Given that,

a) Point estimate = sample mean = = 230

sample standard deviation = s = 11

sample size = n = 25

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

b) At 95% confidence level the t is,

  = 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

t _/2,df = t _{0.025, 24} = 2.064

c) Standard error =SE = (s /n)

= ( 11 / 25)

SE = 2.2

Margin of error = E = t _/2,df * SE

E = 2.064 * 2.2 = 4.54

d) The 95% confidence interval estimate of the population mean is,

- E < < + E

230 - 4.54 < < 230 + 4.54

225.46 < < 234.54

lower bound = 225.46

upper bound = 234.54