Question

TABLE 10-11 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. Referring to Table 10-11, what is/are the critical value(s) when testing whether the current population proportion is higher than before if α = 0.05?

Group of answer choices

± 1.645

+ 1.96

+ 1.645

± 1.96

Answer 1

Sol:

Ho:π1 =π2

since the claim is whether the current population proportion is higher than before

Ha: π1 >  π2

alpha=0.05

since it is right tail

=NORM.S.INV(0.95)

=1.644853627

z critcal value=1.644853627

Z Statistic

z=p1^-p2^/sqrt(p1^*(1-p1^)/n1+p2^*(1-p2^)/n2)

z=(0.66-0.60)/sqrt(0.66*(1-0.66)/150+0.60*(1-0.60)/160))

z=1.096176

z statistic is less thna critical z value

Fail to reject Ho

Accept Ho

No suffcient evidence at 5% level of significance to support the claim

+ 1.645