Question

The business college computing center wants to determine the proportion of business students who have laptop computers. If the proportion exceeds 30%, then the lab will scale back a proposed enlargement of its facilities. Suppose 250 business students were randomly sampled and 75 have laptops. Test if the proportion exceeds 30%. Use significant level alpha: 0.05 ( p value Method)

Answer 1

Solution :

Given that,

= 0.30

1 - = 0.70

n = 250

x = 75

Level of significance = = 0.05

Point estimate = sample proportion = = x / n = 0.3

This a two- tailed test.

The null and alternative hypothesis is,

Ho: p = 0.30

Ha: p 0.30

Test statistics

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

= ( 0.3 - 0.30) / (0.30*0.70) /250

= 0

P-value = P(Z > z )

= 1 - P(Z < 0 )

= 1 - 0.5

= 0.5000

The p-value is p = 0.5000, and since p = 0.5000 > 0.05, 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 the proportion exceeds 30%, at the α = 0.05 significance level.