Answer:
Explained below.
Step-by-step explanation:
(a)
In this case we need to determine if the proportion of customer complaints has decreased by more than 10% under the new packaging design.
The hypothesis can be defined as follows:
<em>H</em>₀: The proportion of customer complaints has not decreased by more than 10% under the new packaging design, i.e. <em>p</em>₁ - <em>p</em>₂ ≤ 0.10.
<em>Hₐ</em>: The proportion of customer complaints has decreased by more than 10% under the new packaging design, i.e. <em>p</em>₁ - <em>p</em>₂ > 0.10.
(b)
The information provided is:
n₁ = 220
n₂ = 220
X₁ = 86
X₂ = 41
Compute the sample proportions and total proportions as follows:
Compute the test statistic value as follows:
The test statistic value is 4.73.
Compute the <em>p</em>-value as follows:
The <em>p</em>-value of the test is 0.
(c)
The decision rule is:
The null hypothesis will be rejected if the p-value of the test is less than the significance level.
<em>p</em>-value = 0 < <em>α</em> = 0.01.
The null hypothesis will be rejected at 1%significance level.
Thus, there is enough evidence at 1% significance level to support the engineers' claim.
(d)
The decision rule is:
The null hypothesis will be rejected if the p-value of the test is less than the significance level.
<em>p</em>-value = 0 < <em>α</em> = 0.10.
The null hypothesis will be rejected at 10%significance level.
Thus, there is enough evidence at 10% significance level to support the engineers' claim.