Question

Use a α = .01 significance level to test the claim that 90% students have a Facebook account. Survey results: n=500, x= 430.

H0=

H1=

Left tail, right tail or two tail? Explain, please!

Test statistic:

P-value:

Conclusion:

Answer 1

Solution :

Given that,

= 0.90

1 - = 0.10

n = 500

x = 430

Level of significance = = 0.01

Point estimate = sample proportion = = x / n = 0.86

This a two- tailed test.

The null and alternative hypothesis is,

Ho: p = 0.90

Ha: p 0.90

Test statistics

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

= ( 0.86 - 0.90) / (0.90*0.10) /500

= -2.981

P-value = 2 * P(Z<z)

= 2 * P(Z <z )

= 2*P(Z < -2.981)

= 1 - 0.0014

= 0.0028

The p-value is p = 0.0028, and since p = 0.0028 < 0.01, it is concluded that the null hypothesis is rejected.

Conclusion:

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that t 90% students have a Facebook account, at the α = 0.01 significance level.