Question

) The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion exceeds 25%, then the lab will scale back a proposed enlargement of its facilities. Suppose 200 business students were randomly sampled and 65 have PC's at home. Use the appropriate statistic to decide if there is a need for an enlargement of its facility. Use a leel of siignificance of = 0.01.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p =0.25

H_a : p > 0.25

= x / n = 65 / 200 = 0.325

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

=0.325 - 0.25 / [(0.25 * 0.75) / 200]

= 2.45

P-value = 0.0072

= 0.01

P-value <

Reject the null hypothesis .

There is sufficient evidence to suggest that the proportion exceeds 25% .