For problem 8–55, give a 95% confidence interval for the difference in proportion of theaters nationwide where one movie will be preferred over the other. Is the point 0 contained in the interval?...

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For problem 8–55, give a 95% confidence interval for the difference in proportion of theaters nationwide where one movie will be preferred over the other. Is the point 0 contained in the interval? Discuss.

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.

Answered Same DayDec 25, 2021

Answer To: For problem 8–55, give a 95% confidence interval for the difference in proportion of theaters...

Robert answered on Dec 25 2021

126 Votes

If CI for difference of two parameters contains value zero, it is plausible that the
two parameters are equal.
It is plausible that the success rate is equal for both cinema halls.
95% CI for p1 − p2
x1 = 60, n1 = 80, x2 = 65, n2 = 100
p̂1 =
60
80 = 0.75,
p̂2 =
65
100 = 0.65
(p̂1 − p̂2) = (0.75 − 0.65) = 0.1
SEp1−p2 =
√
p̂1(1 − p̂1)
n1
+ p̂2(1 − p̂2)
n2
=
√
0.75(0.25)
80...

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For problem 8–55, give a 95% confidence interval for the difference in proportion of theaters nationwide where one movie will be preferred over the other. Is the point 0 contained in the interval?...

Answer To: For problem 8–55, give a 95% confidence interval for the difference in proportion of theaters...

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