# 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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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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