A 95% confidence interval for the difference in mean revenue at the box office for drama and comedy movies is (7.44, 72.56).
We have given that,
Sample mean of peoples who like drama , x₁-bar = 190
Sample mean of peoples who like comedy,x₂-bar = 150
Sample size for darama sample, n₁ = 17
Sample size for comedy sample, n₂ = 14
Standard deviations, s₁ = 60
Standard deviations, s₂ = 30
Confidence level = 0.95 or 95%
Using Z-table , Z-score for 95% confidence level is 1.96..
We have to calculate a 95% confidence interval for the difference in mean revenue at the box office for drama and comedy movies.
It is given by following Confidence interval formula,
x₁-bar - x₂-bar ± Z ( √(s₁²/n₁ + s₂²/n₂))
= 190 - 150 ± 1.96(√(60²/17 + 30²/14))
= 40 ± 1.96(√3600/17 + 900/14))
= 40 ± 32.56
= (7.44, 72.56)
Hence, the required 95% confidence interval is
(7.44, 72.56) .
To learn more about Confidence interval, refer:
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Complete question:
A Hollywood studio believes that a movie that is considered a drama will draw a larger crowd on average than a movie that is considered a comedy. To test this theory. the studio randomy selects several movies that are classified as dramas and several movies that are classified as comedies and determines the box office revenue for. each movie. The results of the survey are as follows. Assurne that the population variances are approximately equal, Calculate a
95%
confidence interval for the difference in mean revenue at the box office for drama and comedy movies: Let dramas be Population-1 and comedies be Population 2. Write your answer using interval notation and round the interval endpoints to two decimal places
