Hypothesis Testing Using Alpha and Significance Levels
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1) A trucking firm suspects that the mean lifetime of a certain tire uses is less than 35,000miles. To check the claim the firm randomly selects and tests 54 of these tires and gets a mean life time of 34,570 with a standard deviation of 1200 miles. At a alpha = 0.05 test the trucking firms claims.
2) A local brewery distributes beer in bottles labeled 12 ounces. A government agency thinks that the brewery is cheating it's customers. The agency selects 20 of these bottles, measure their contents, and obtain a sample mean 11.7 ounces with a standard deviation of 0.7 ounces. Use a 0.01 significance level to test the agency's claim that the brewery is cheating it's customers.
3) A local group claims that the police issue at least 60 speeding tickets a day in their area. To prove their point they randomly selected 2 weeks. Their research yields the number of tickets issued for each day. The data is listed below. At alpha = 0.01, test the group's claims using P-values.
70,48,41,68,69,55,70,57,60,83,32,60,72,58.
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Solution Summary
This response provides guidelines on checking claims using alphas, significance levels, and p-values.
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3 Claims
1) A trucking firm suspects that the mean lifetime of a certain tire uses is less than 35,000miles. To check the claim the firm randomly selects and tests 54 of these tires and gets a mean life time of 34,570 with a standard deviation of 1200 miles. At a alpha =0.05 test the trucking firms claims.
H0: Mean life time ≥ 35000 miles
H1: Mean life time < 35000 miles
The test Statistic used is
Decision rule: Reject the null hypothesis, if the calculated value of test statistic is less than the critical value of t at 0.05 significance level.
Details
t Test for Hypothesis of the Mean
Data
Null Hypothesis μ= 35000
Level of Significance 0.05
Sample Size 54
Sample Mean 34570
Sample Standard Deviation 1200
Intermediate Calculations
Standard Error of the Mean 163.2993162
Degrees of Freedom 53
t Test Statistic -2.633201473
...
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