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 Toys4Tots, a large toy manufacturer, wants to evaluate the effectiveness of a new packaging design which engineers claim will reduce customer complaints by more than 10 percentage points. Customer satisfaction surveys were sent to 200 parents who registered toys packaged under the old design and 200 parents who registered toys packaged under the new design. Of these, 85 parents expressed dissatisfaction with packaging of the old design, and 40 parents expressed dissatisfaction with packaging of the new design.

Let p₁ 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.

	H0: p1 – p2 ≤ 0.10; HA: p1 – p2 > 0.10
	H0: p1 – p2 = 0.10; HA: p1 – p2 ≠ 0.10
	H0: p1 – p2 ≥ 0.10; HA: p1 – p2 < 0.10

b. What is the value of the test statistic and the associated p-value? (Round your sample proportions to 3 decimal places. Round all other intermediate calculations to at least 4 decimal places.)

Test statistic
p-value

c. At the 5% significance level, do the results support the engineers’ claim?

(Click to select)(Yes/No), the results (Click to select)(support/do not support )the engineer’s claim that the new package design reduces customer complaints by more than 10%.

d. At the 1% significance level, do the results support the engineers’ claim?

(Click to select)(Yes/No), the results (Click to select)(support/do not support) the engineer’s claim that the new package design reduces customer complaints by more than 10%.

Answer 1