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    P-Value

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    Please provide step by step instructions on how to solve the following problems using actual numbers provided. Thanks

    1) A student representative claims that 60% of the students favor a move to division 1. A random sample of 250 students were selected and 140 of them indicated they favored a move to division 1.
    a. Perform the appropriate test of hypothesis to test the representative's claim. Use alpha=.05.
    b. Write out each step in determining the p-value for the test in part one.

    2) The manager of a movie rental store was interested in examining the relationship between the weekly take-home pay for a family and the amount that family spends weekly on recreational activites. The following output was generated using Minitab:
    Covariances

    takehome 4413.84
    recreation 2419.64 1364.29

    Let 2=weekly take-home pay and y=amount spent weekly on recreational activities
    a. identify s of x squared (=4413.84)
    b. s of xy (=1364.29)
    c. s of y squared (=2419.64)
    d. calculate the correlation between weekly take-home pay and amount spent weeky on recreational activities.
    e. Interpret the correlation coefficient found in part d.

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    Solution Preview

    1) Solution. Let us define two hypothesis.
    <br> H0: p=0.6; H1:p is not equal to 0.6
    <br>where p is the probability that the students favor a move to division 1.
    <br>
    <br> We define the following random variables Xi, i=1,2,...,250, where
    <br>Xi=1 if the ith people favor a move to division 1; otherwise Xi=0, i=1,2,...,250.
    <br>
    <br>If the hypothesis H0 is true, then by the laws of large numbers in probability we know that X*=(X1+X2+...+X250)/250 should approximately follow normal distribution ...

    Solution Summary

    The solution addresses - 1) A student representative claims that 60% of the students favor a move to division 1. A random sample of 250 students were selected and 140 of them indicated they favored a move to division 1.
    a. Perform the appropriate test of hypothesis to test the representative's claim. Use alpha=.05.
    b. Write out each step in determining the p-value for the test in part one.

    2) The manager of a movie rental store was interested in examining the relationship between the weekly take-home pay for a family and the amount that family spends weekly on recreational activites. The following output was generated using Minitab:
    Covariances

    takehome 4413.84
    recreation 2419.64 1364.29

    Let 2=weekly take-home pay and y=amount spent weekly on recreational activities
    a. identify s of x squared (=4413.84)
    b. s of xy (=1364.29)
    c. s of y squared (=2419.64)
    d. calculate the correlation between weekly take-home pay and amount spent weeky on recreational activities.
    e. Interpret the correlation coefficient found in part d.

    $2.49

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