Question

2. Technology is dramatically changing the way we communicate. In 1997, a survey of 880 U.S. households showed that 149 of them use e-mail. Use those sample test results to test the claim that more that 15% of U.S. households use e-mail. Use a 0.01 significance level. Show all work and write an english response.

Answer 1

Solution :

Given that,

= 0.15

1 - = 0.85

n = 880

x = 149

Level of significance = = 0.01

Point estimate = sample proportion = = x / n = 0.169

This a right (One) tailed test.

The null and alternative hypothesis is,

Ho: p = 0.15

Ha: p 0.15

Test statistics

z = ( - ) / *(1-) / n

= ( 0.169 - 0.15) / (0.15*0.85) / 880

= 1.578

Critical value of  the significance level is α = 0.01, and the critical value for a right-tailed test is

= 2.33

Since it is observed that z = 1.578 < = 2.33, it is then concluded that the null hypothesis is fail to rejected.

P-value = P(Z>z)

= 1 - P(Z <z )

= 1- P(Z < 1.578)

= 1 - 0.9427

= 0.0573

The p-value is p = 0.0573, and since p = 0.0573 > 0.01, it is concluded that the null hypothesis is fail to rejected.

Conclusion:

It is concluded that the null hypothesis Ho is fail to rejected. Therefore, there is not enough evidence to claim that more that 15% of U.S. households use e-mail. at the α = 0.01 significance level.