Question

A national magazine took a poll to determine company's opinions about outsourcing. Outsourcing is defined as the assignment of critical, but non-core, business functions to outside specialists. The magazine found that 26 percent of business executives felt that the benefits of outsourcing were less than what they expected. A sample of 100 business executives was polled. In this sample 19% of the business executives felt the benefits of outsourcing were less than what they expected. You want to determine whether the proportion of business executives in the sample differs from the national magazine poll. Which statistical test should you use?

Answer 1

Hypothesis test on a proportion.

There is no enough evidence to support the claim that the proportion of business executives in the sample differs from the national magazine poll.

Explanation:

We should test the hypothesis of the proportion, with a z-statistic.

The claim is that the proportion of business executives in the sample differs from the national magazine poll.

Then, the null and alternative hypothesis are:

`H_0: \pi=0.26\\\\H_a:\pi<0.26`

The significance level is assumed to be 0.05.

The sample, of size n=100, has a proportion p=0.19.

The standard error for the proportion is:

`\sigma_p=\sqrt{(\pi(1-\pi))/(n)}=\sqrt{(0.26*0.74)/(100)}=√(0.001924)=0.044`

Then, the z-statistic can be calculated as:

`z=(p-\pi+0.5/n)/(\sigma_p)=(0.19-0.26+0.5/100)/(0.044)=(-0.065)/(0.044)=-1.477`

The P-value for this one-tailed test is:

`P-value=P(z<-1.477)=0.07`

As the P-value is bigger than the significance level, the effect is not significant. The null hypothesis failed to be rejected.

There is no enough evidence to support the claim that the proportion of business executives in the sample differs from the national magazine poll.