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 that engineers claim will reduce customer complaints by more than 10 percentage points. Customer satisfaction surveys were sent to 250 parents who registered toys packaged under the old design and 250 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.

 

multiple choice 1

• H₀: p₁ – p₂ ≤ 0.10; H_A: p₁ – p₂ > 0.10

• H₀: p₁ – p₂ = 0.10; H_A: p₁ – p₂ ≠ 0.10

• H₀: p₁ – p₂ ≥ 0.10; H_A: 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.)

 

b-2. Find the p-value.

 

multiple choice 2

• p-value < 0.01

• 0.01 ≤ p-value < 0.025

• 0.025 ≤ p-value < 0.05

• 0.05 ≤ p-value < 0.10

• p-value ≥ 0.10

 

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

 

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

 

Answer 1

The statistical software output for this problem is:

From above output:

Test statistic = 2.11