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Answer:
We conclude that there is no difference in the two population proportions using α = 0.05.
Step-by-step explanation:
We are given that a corporation randomly selects 150 salespeople and finds that 66% who have never taken a self- improvement course would like to do so.
The firm did a similar study 10 years ago and found that 70% of a random sample of 160 salespeople wanted a self-improvement course.
Let = <u><em>true proportion of workers who would like to attend a self-improvement course in the recent study.</em></u>
= <u><em>true proportion of workers who would like to attend a self-improvement course in the past study.</em></u>
SO, Null Hypothesis, :
{means that there is no difference in the two population proportions}
Alternate Hypothesis, :
{means that there is a difference in the two population proportions}
The test statistics that would be used here <u>Two-sample z test for</u> <u>proportions</u>;
T.S. = ~ N(0,1)
where, = sample proportion of salespeople who would like to attend a self-improvement course in recent study = 66%
= sample proportion of salespeople who would like to attend a self-improvement course in past study = 70%
= sample of salespeople in recent study = 150
= sample of salespeople in past study = 160
So, <u><em>the test statistics</em></u> =
= -0.755
The value of z test statistics is -0.755.
<u>Now, at 0.05 significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.</u>
Since our test statistic lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u><em>we fail to reject our null hypothesis</em></u>.
Therefore, we conclude that there is no difference in the two population proportions.