Question

The Pew Internet and American Life Project reports that young people ages 12-17 send a mean of 60 text messages per day. A random sample of 40 young people showed a sample mean of 69 texts per day. Assumeσ = 28 for the population.

Using a significance level of α = 0.01, test whether the population mean number of text messages per day differs from 60.

What is the null hypothesis? What is the alternative hypothesis? Which kind of test is this (left-tail, right-tail, or two-tail)?

Find z data, Find the critical region.

Do we reject the null hypothesis or fail to reject it?

Answer 1

The null and alternative hypothesis are

H0: = 60

Ha: 60

This is two tailed test.

Test statistics

z = ( - ) / ( / sqrt(n) )

= (69 - 60) / ( 28 / sqrt( 40) )

= 2.03

Critical values at 0.01 level = -2.576 , 2.576

Critical region = Reject H0 if z < -2.576 OR z > 2.576

Since test statistics falls in non-rejection region, We fail to reject H0