u BlazerNET Assignments: FA2017 QI × / D Assignment 2B C ezto.mheducation.com/hm
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u BlazerNET Assignments: FA2017 QI × / D Assignment 2B C ezto.mheducation.com/hm.tpx?--0.8304305965477946-1509307565838 value: 0.00 points 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 220 parents who registered toys packaged under the old design and 220 parents who registered toys packaged under the new design. Of these, 84 parents expressed dissatisfaction with packaging of the old design, and 42 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 for whether the proportion of customer complaints has decreased by more than 10% under the new packaging design Ho: p1-p% 0.10, HA, p1-p2 > 0.10 O HoPr-p,-0.10; HA pl-P2 # 0.10 O Ho p1-P220.10, HA P1-p20.10 b. What is the value of the test statistic and the associated p-value? (Round intermediate calculations to at least 4 decimal places. Round "Test statistic" value to 2 decimal places and "p-value" to 4 decimal places.) Test statistic p- value 0.00 C. At the 10% significance level, do the results support the engineers' claim? Yes , the results 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? 0 , the results do not support the engineers claim that the new package design reduces customer complaints by more than 10%. References eBook &Resources; Worksheet Difficulty: 3 Hard Learning Objective: 10-03 Make inferences about the difference between two population proportions based on independent samplingExplanation / Answer
The statistical software output for this problem is:
Two sample proportion summary hypothesis test:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0.1
HA : p1 - p2 > 0.1
Hypothesis test results:
Hence,
Test statistic = 2.11
p - Vaue = 0.0175
Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value p1 - p2 84 220 42 220 0.19090909 0.043102363 2.109144 0.0175Related Questions
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