Two brands of tires were compared for the proportion of defective tires. Random samples of tires were collected from each brand, and the number of defective tires from each brand was recorded. The data is in the following table. nNumber of defective tires (x) 41 Continental Michelin 320 180 32 a.Construct a 97% confidence interval for the difference between the two proportions. b.For part a, find the desired sample sizes if you want the Continental sample to be 1.5 times Michelin sample with a sampling error equal to 0.03. c. Conduct a test of hypothesis to determine if the defective rates are the same. Use the P-value to interpret the results (a is not given).

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 58E: What is meant by the sample space of an experiment?
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Two brands of tires were compared for the proportion of defective tires. Random samples of tires
were collected from each brand, and the number of defective tires from each brand was recorded. The
data is in the following table.
Number of defective tires (x)
41
32
n
Continental
Michelin
320
180
a.Construct a 97% confidence interval for the difference between the two proportions.
b.For part a, find the desired sample sizes if you want the Continental sample to be 1.5 times Michelin
sample with a sampling error equal to 0.03.
c. Conduct a test of hypothesis to determine if the defective rates are the same. Use the P-value to
interpret the results (a is not given).
Transcribed Image Text:Two brands of tires were compared for the proportion of defective tires. Random samples of tires were collected from each brand, and the number of defective tires from each brand was recorded. The data is in the following table. Number of defective tires (x) 41 32 n Continental Michelin 320 180 a.Construct a 97% confidence interval for the difference between the two proportions. b.For part a, find the desired sample sizes if you want the Continental sample to be 1.5 times Michelin sample with a sampling error equal to 0.03. c. Conduct a test of hypothesis to determine if the defective rates are the same. Use the P-value to interpret the results (a is not given).
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