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    Using the "Traditional" and "P-Value" Method for Hypotheses

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    In both "traditional" and "p- value" method: A simple random sample of 40 recorded speeds(in mi/h) is obtained from cars traveling on a section of highway 405 in Los Angeles. The simple random sample has a mean of 68.4mi/h and a standard deviation of 5.7mi/h. Use a 0.05 significance level to test the claim that the mean speed of all cars is greater than the posted speed limit of 65 mi/h.

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    Since the sample size is fairly large (n > 30), we use normal distribution.
    The null hypothesis tested is
    H0: Mean speed of all cars ≤ 65 mi/h. (µ ≤ 65)
    The alternative hypothesis is
    H1: Mean speed of all cars > 65 mi/h. (µ > 65)
    Significance level = 0.05
    The test statistic used is Z = x̅ - µ/σ / √ n, where = 68.4, n = 40, σ = 5.7
    Therefore, Z = 68.4 - 65/ 5.7 /√40 = 3.77254177
    Traditional Method
    Rejection criteria: Reject the null ...

    Solution Summary

    Using the "Traditional" and "P-Value" Method for Hypotheses is examined.