A product testing laboratory selected a sample of 20 printers from two different manufacturers to determine if they could print more than 100,000 pages without breaking down.At = .05, test the claim
That the proportions of printers from Manufacturer 1 and Manufacturer 2 that lasted for more than
100,000 pages are equal.
A)There is not evidence to reject the claim that the proportions are equal because the test value 2.506 3.841
B)There is evidence to reject the claim that the proportions are equal because the test value 3.841 1.003
C)There is not evidence to reject the claim that the proportions are equal because the test value 2.506 9.488
D)There is not evidence to reject the claim that the proportions are equal because the test value 9.488 1.003

Question

A product testing laboratory selected a sample of 20 printers from two different manufacturers to determine if they could print more than 100,000 pages without breaking down.At = .05, test the claim
That the proportions of printers from Manufacturer 1 and Manufacturer 2 that lasted for more than
100,000 pages are equal. 
A)There is not evidence to reject the claim that the proportions are equal because the test value 2.506 3.841 
B)There is evidence to reject the claim that the proportions are equal because the test value 3.841 1.003 
C)There is not evidence to reject the claim that the proportions are equal because the test value 2.506 9.488 
D)There is not evidence to reject the claim that the proportions are equal because the test value 9.488 1.003

Quizplus · Accepted Answer

The null hypothesis is that the proportions of printers from both manufacturers that lasted for more than 100,000 pages are equal. The alternative hypothesis is that they are not equal. Since we are testing for proportions, we use a two-sample z-test for proportions. The test value calculated is 2.506, which corresponds to a p-value of 0.0123. Since the p-value is less than the significance level of 0.05, we reject the alternative hypothesis and conclude that there is not sufficient evidence to claim that the proportions are different. Therefore, we do not reject the null hypothesis that the proportions are equal. Choice A is the correct answer. Based on the given test value of 2.506 and the critical value of 3.841, we fail to reject the null hypothesis which states that the proportions of printers from both manufacturers that can print more than 100,000 pages are equal. Therefore, there is not enough evidence to support the claim that the proportions are different.

A Product Testing Laboratory Selected a Sample of 20 Printers