Question

The business college computing center wants to determine the proportion of business students who have laptop computers. If the proportion differs from 30%, then the lab will modify a proposed enlargement of its facilities. Suppose a hypothesis test is conducted and the test statistic is 2.5. Find the p-value for a two-tailed test of hypothesis.

Answer 1

Answer: 0.0124

Explanation:

Let p be the proportion of business students who have laptop computers.

As per given , we have to test hypothesis:

`H_0:p=0.30\\H_a:p\\eq0.30`

Since the alternative hypothesis two-tailed , so the test is a two-tailed test.

We assume that this is a case for normal distribution.

For proportion , we use z-test .

P-value for two-tailed test = 2P(Z>|z|)=2P(Z>|2.5|)

=2P(Z>2.5)=2(1-P(Z<2.5)) [∵ P(Z>z)=1-P(Z≤z)]

=2(1-0.9938) [By z-table]

= 2(0.0062)

= 0.0124

Hence, the p-value for a two-tailed test of hypothesis= 0.0124