A metropolitan transportation authority has set a bus mechanical reliability goal of 3,800 bus miles. Bus mechanical reliability is measured

Question

A metropolitan transportation authority has set a bus mechanical reliability goal of 3,800 bus miles. Bus mechanical reliability is measured specifically as the number of bus miles between mechanical road calls. Suppose a sample of 100 of 100 buses resulted in a sample mean of 3850 bus miles and a sample standard deviation of 275 bus miles. Please show your work.

A. T-stat=

B. The critical values is/are?

C. Is there sufficient evidence to reject the null hypothesis using a=0.05.

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Clara 1 week 2021-11-25T12:29:00+00:00 1 Answer 0 views 0

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    2021-11-25T12:30:29+00:00

    Answer:

    (A) T-stat = 1.82

    (B) Critical value is 1.645

    (C) Yes, there is sufficient evidence to reject the null hypothesis using a 0.05 significance level.

    Step-by-step explanation:

    (A) T-stat (z) = (sample mean – population mean) ÷ sd/√n

    sample mean = 3850 bus miles

    population mean = 3800 bus miles

    sd = 275 bus miles

    n = 100

    z = (3850 – 3800) ÷ 275/√100 = 50 ÷ 275/10 = 50 ÷ 27.5 = 1.82

    (B) The test is a one-tailed test. The critical value is obtained from the standard normal distribution table. The critical value using a 0.05 significance level is 1.645

    (C) Null hypothesis: The bus mechanical reliability is 3850 bus miles.

    Alternate hypothesis: The bus mechanical reliability is less than 3850 bus miles.

    Conclusion:

    There is sufficient evidence to reject the null hypothesis because the test statistic (1.82) is greater than the critical value (1.645)

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