Question

A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let π1 and π2 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively. If the firm wanted to test whether this proportion has changed from the previous study, which represents the relevant hypotheses?

Answer 1

Null hypotheses :
`\pi_1=\pi_2`

Alternative hypotheses :
`\pi_1\\eq\pi_2`

Explanation:

Let
`\pi_1` and
`\pi_2` represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.

If the firm wanted to test whether this proportion has changed from the previous study.

Since null hypotheses shows there is no difference between the groups whether alternative hypotheses shows there is significance difference.

Then, the required hypotheses will be:-

Null hypotheses :
`\pi_1=\pi_2`

Alternative hypotheses :
`\pi_1\\eq\pi_2`