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 pi1 and pi2 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively. At alpha = 0.10, the critical value when testing whether the population proportions are different is _____ and the value of the computed test statistic to use in evaluating the alternative hypothesis that there is a difference in the two population proportions is _____.

		a. 3.842 … 4.335
		b. 3.842 … 2.706
		c. 2.706 … 1.194
		d. 2.706 … 0.274

Answer 1

Solution :

n1 = 150 , p1^ = 66% = 0.66 ,n2 = 160 , p2^ = 60% = 0.60

α = 0.10

p bar = (n1p1^ + n2p2^)/(n1+n2) = 0.6290

b bar = 1 - p bar = 0.3710

Alternative hypothesis : there is a difference in the two population proportions

Ho: p1 = p2

Ha : p1 ≠ p2

Critical value = 1.645 ( Using Table )

Test statistic = (p1^ - p2^)/√(((pbar * q bar)/n1)+((pbar*q bar)/n2))) = 1.093

At alpha = 0.10, the critical value when testing whether the population proportions are different is 1.645 and the value of the computed test statistic to use in evaluating the alternative hypothesis that there is a difference in the two population proportions is 1.093

Answer :

1.645 .... 1.093

The provieded options are incorrect. please check with instructor.