Information about movie ticket sales was printed in a movie magazine. in a sample of of fifty pg-rated movies, 36% had ticket sales in excess of $30,000,000. in a sample of thirty-five r-rated movies, 23% grossed over $30,000,000. suppose that this data is used to test the claim that the proportion of movies with ticket sales in excess of $30,000,000 is the same for pg movies as it is for r-rated movies. what would be the test statistic for this test? z = 1.29 z = 2.07 z = 4.005 z = 2.58

Question

Mathematics

Imani Li

25 July, 22:11

Information about movie ticket sales was printed in a movie magazine. in a sample of of fifty pg-rated movies, 36% had ticket sales in excess of $30,000,000. in a sample of thirty-five r-rated movies, 23% grossed over $30,000,000. suppose that this data is used to test the claim that the proportion of movies with ticket sales in excess of $30,000,000 is the same for pg movies as it is for r-rated movies. what would be the test statistic for this test? z = 1.29 z = 2.07 z = 4.005 z = 2.58

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Zoey · Answer 1

Let us say that the samples for fifty movies is 1 and samples for thirty five is 2. To solve the test statistic z, we can use the formula:

z = (p1 - p2) / sqrt [p (1 - p) (1 / n1 + 1 / n2) ]

Where,

p1 = is the proportion for sample 1 = 0.36

p2 = is the proportion for sample 2 = 0.23

n1 = number of samples = 50

n2 = number of samples = 35

while p can be calculated using the formula:

p = [p1 * n1 / (n1 + n2) ] + [p2 * n2 / (n1 + n2) ]

p = [0.36 * 50 / (50 + 35) ] + [0.23 * 35 / (50 + 35) ]

p = 0.211764705 + 0.094705882

p = 0.306470587

Going back for the calculation of z:

z = (0.36 - 0.23) / sqrt [0.306 (1 - 0.306) (1 / 50 + 1 / 35) ]

z = 1.279

Therefore the nearest answer is:

z = 1.29