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# Independent sample t test

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.

#### Solution Preview

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.

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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