Explore BrainMass

Explore BrainMass

    Hypothesis Testing Using Alpha and Significance Levels

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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.

    © BrainMass Inc. brainmass.com June 3, 2020, 9:32 pm ad1c9bdddf
    https://brainmass.com/statistics/hypothesis-testing/hypothesis-testing-alpha-significance-levels-187633

    Solution Preview

    Please see the attachments for the solutions.

    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
    ...

    Solution Summary

    This response provides guidelines on checking claims using alphas, significance levels, and p-values.

    $2.19

    ADVERTISEMENT