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    Hypothesis Testing: Pinnacle Fitness Project

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    Please help in understanding how to formulate null and alternative hypotheses for each of the statistics provided
    Treat their statistics as population values to be tested.
    Assist in writing a summary of your findings and discuss how the customer base (population) may have changed in seven years.
    What do these changes mean for marketing strategy? How can company capitalize on the analyst's findings?

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    The firm's report can be analyzed as follows:
    The average household income is less than $65,000.
    The null hypothesis tested is
    H0: Mean household income ≥ $65,000 (µ ≥ $65,000)
    The alternative hypothesis is
    H1: Mean household income < $65,000 (µ < $65,000)
    Significance level = 0.05
    Test Statistic used is given that = 71,027, n = 250, s = 15,782.01389,  = 65,000
    Therefore, = 6.04
    Decision rule: Reject the null hypothesis, if the observed significance (p-value) is less than the significance level 0.05.
    P-value = P (t249 < 6.04) = 1.000
    Conclusion: Fails to reject the null hypothesis, since the observed significance (p-value) is greater than the significance level 0.05. The sample does not provide enough evidence to support the firm's claim that the mean household income is less than $65,000.
    Minitab output
    One-Sample T: Income

    Test of mu = 65000 vs < 65000

    95% Upper
    Variable N Mean StDev SE Mean Bound T P
    Income 250 71027 15782 998 72675 6.04 1.000

    Hence it is clear that there is a significant increase in the household income over the seven years. In other words, there ...

    Solution Summary

    The solution provides a step-by-step method for the calculation of testing an hypothesis. Formula for the calculation and interpretation of the results are also included.