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10 March, 02:42

A shareholders' group, in lodging a protest, claimed that the mean tenure for a chief executive officer (CEO) was at least nine years. A survey of companies reported in The Wall Street Journal found a sample mean tenure of x = 7.67 years for CEOs with a standard deviation of s = 6.38 years. (a) Choose the correct hypotheses that can be used to challenge the validity of the claim made by the shareholders' group. H0: μ - Select your answer - years Ha: μ - Select your answer - years (b) Assume that 85 companies were included in the sample. What is the p value for your hypothesis test? If required, round your answer to four decimal places. (c) At α = 0.01, what is your conclusion? We - Select your answer - the null hypothesis. We - Select your answer - conclude that the mean tenure for a CEO is shorter than nine years.

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  1. 10 March, 03:59
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    Step-by-step explanation:

    a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

    For the null hypothesis,

    H0:µ ≥ 9

    For the alternative hypothesis,

    Ha:µ < 9

    This is a left tailed test.

    b) Since the population standard deviation is not given, the distribution is a student's t.

    Since n = 85,

    Degrees of freedom, df = n - 1 = 85 - 1 = 84

    t = (x - µ) / (s/√n)

    Where

    x = sample mean = 7.67

    µ = population mean = 9

    s = samples standard deviation = 6.38

    t = (7.67 - 9) / (6.38/√85) = - 1.92

    We would determine the p value using the t test calculator. It becomes

    p = 0.029

    c) α = 0.01

    Since α, 0.01 < the p value, 0.029, then we would fail to reject the null hypothesis. Therefore, At a 1% level of significance, there was no significant evidence that the the mean tenure for a CEO is shorter than nine years.
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