Question

10. A salesman for a new manufacturer of cellular phones claims not only that they cost the retailer less but also that the percentage of defective cellular phones found among his products, ( p1 ), will be no higher than the percentage of defectives found in a competitor's line, ( p2 ). To test this statement, the retailer took a random sample of 215 of the salesman's cellular phones and 210 of the competitor's cellular phones. The retailer found that 22 of the salesman's cellular phones and 7 of the competitor's cellular phones were defective. Does the retailer have enough evidence to reject the salesman's claim? Use a significance level of α=0.01 for the test.

Step 1 of 6: State the null and alternative hypotheses for the test.

Step 2 of 6: Find the values of the two sample proportions, pˆ1 and pˆ2. Round your answers to three decimal places.

Step 3 of 6: Compute the weighted estimate of p, p‾. Round your answer to three decimal places.

Step 4 of 6: Compute the value of the test statistic. Round your answer to two decimal places

Step 5 of 6: Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to two decimal places

Step 6 of 6: Make the decision for the hypothesis test.

Answer 1

Step 1 of 6:

null Hypothesis:               Ho:		p1-p2	<=	0.0000
alternate Hypothesis:    Ha:		p1-p2	>	0.0000

Step 2 of 6: p^1 =0.102

p^2 =0.033

Step 3 of 6: Compute the weighted estimate of p, =0.068

Step 4 of 6: Compute the value of the test statistic   =2.83

Step 5 of 6: Decision rule:reject HO if z>2.33

Step 6 of 6: reject null hypothesis