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. Assume σ = 28 for the population.

Using a significance level of α = 0.05, test whether the population mean number of text messages per day is greater than 60.

i. What is the null hypothesis?
ii. What is the alternative hypothesis?

iii. Which kind of test is this (left-tail, right-tail, or two-tail)? iv. Find zdata.

v. Find the critical region.
vi. Do we reject the null hypothesis or fail to reject it?

Answer 1

Solution :

Given that,

Population mean = = 60

Sample mean = = 69

Population standard deviation = = 28

Sample size = n = 40

Level of significance = = 0.05

This a right (One) tailed test.

The null and alternative hypothesis is,  

Ho: 60

Ha: 60

Critical value of  the significance level is α = 0.05, and the critical value for a right-tailed test is

= 1.64

The test statistics,

Z =( - )/ (/n)

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

= 2.033

Since it is observed that z = 2.033 > , = 1.64 ,it is then concluded that the null hypothesis is rejected.