Question

In an effort to make children's toys safer and more tamperproof, toy packaging has become cumbersome for parents to remove in many cases. Accordingly, the director of marketing at Toys4 Tots, a large toy manufacturer, wants to evaluate the effectiveness of a new packaging design that engineers claim will reduce customer complaints by more than 10 percentage points. Customer satisfaction vho registered toys packaged under the old design and 230 parents who registered toys packaged under the new design. Of these, 81 parents expressed dissatisfaction with packaging of the old design, and 42 parents expressed dissatisfaction with packaging of the new design. Let p, represent the population proportion of parents that expressed dissatisfaction with the packaging of the old design and p2 represent the population proportion of parents that expressed dissatisfaction with the packaging of the new design. a. Specify the null and alternative hypotheses to test whether customer complaints have been reduced by more than 10 percentage points under the new packaging design. Ho: P1-P2s 0.10; HA P1-P2> 0.10 Ho: P1-P2=0.10; HA P1-P2+0.10 Ho: P1-P22 0.10; HA P1-P2<0.10 b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic b-2. Find the p-value. 0.025 s p-value < 0.05 0.01 s p-value < 0.025 p-value < 0.01 pvalue 20.10 0.05 s p-value <0.10 c. At the 1% significance level, do the results support the engineers' claim? the results the engineer's claim that the new package design reduces customer complaints by more than 10%. d. At the 5% significance level, do the results support the engineers' claim? the results the engineer's claim that the new package design reduces customer complaints by more than 10%.

Answer 1

Answer: na Ho: P,- 12 20.10; HA P - P220.10 hệ - 0 35 22 - a -40 = 0.1826 - Test-Statistic = (P. - P2) - o.) Vēl (1-P). Ê, O-Pa] (0.3522 -0.1826) -0.1 10.35224(1-0.3522) 0.1826 * (-0.1826) 230 230 -1.7182 = 1:72 6-2) p-value of 0.0431 0.02 g s P-value < 0.05 c) at 1.t. level, p-value * 0.01 Accept the null hypothesis.

The results does not support the engineer's claim that the new package design reduces Customer Complaints by more than 101 d) At 57 level, p-value 20.05 Reject the null hypothesis. The results support the engsneer's claim.