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    Independent sample t test

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    Problem 8-55

    Two movies were screen-tested at two different samples of theaters. Mystic river was viewed at 80 theaters and was considered a success in terms of box office sales in 60 of these theaters. Swimming Pool was viewed at a random sample of 100 theaters and was considered a success in 65. Based on these data, do you believe that one of these movies was a greater success than the other? Explain.

    Problem 8-72

    The New York Times reports that cosmetic surgery is seeing much growth recently as the US population ages. One aspect of this growth is that more men are choosing to have plastic surgery to improve their looks. If a random sample of 3,000 men reveals that 140 of them have had plastic surgery, and an independent random sample of 3,000 women reveals that 351 of them have had plastic surgery, test for equality of proportions. Use the 0.05 level of significance.

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    https://brainmass.com/statistics/students-t-test/independent-sample-test-population-189018

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    Chapter 8 Comparison of Two Populations

    Problem 8-55

    Two movies were screen-tested at two different samples of theaters. Mystic river was viewed at 80 theaters and was considered a success in terms of box office sales in 60 of these theaters. Swimming Pool was viewed at a random sample of 100 theaters and was considered a success in 65. Based on these data, do you believe that one of these movies was a greater success than the other? Explain.

    Answer

    The null hypothesis tested is
    H0: There is no significant difference in the proportion of success of the two movies (P1=P2).

    H1: The proportion of success for Mystic River was greater than the proportion of success of Swimming Pool (P1>P2).
    Test statistic

    The test Statistic used is
    where
    Given that P1 = 60/ / 588, P2=65/100 , n1= 80, n2=100

    Z Test for Differences in Two Proportions

    Data
    Hypothesized Difference 0
    Level of Significance 0.05
    Group 1 Mystic River
    Number of Successes 60
    Sample Size 80
    Group 2 : Swimming Pool
    Number of Successes 65
    Sample Size 100

    Intermediate Calculations
    Group 1 Proportion 0.75
    Group 2 Proportion 0.65
    Difference in Two Proportions 0.1
    Average Proportion 0.694444444
    Z Test Statistic 1.447254454

    Upper-Tail Test
    Upper Critical Value 1.644853627
    p-Value 0.073912835
    Do not reject the null hypothesis

    Conclusion: Fails ...

    Solution Summary

    Step by step method for testing the hypothesis under 5 step approach is discussed here.

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