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 randomly 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. Assume that the population variances are approximately equal. Box Office Revenues (Millions of Dollars) | | n | x? | s | | :--- | :--- | :--- | :--- | | Drama | 15 | 190 | 50 | | Comedy | 18 | 160 | 30 | Calculate a 99 % 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.
Added by James B.
Close
Step 1
Sample mean for drama movies (x̄1) = 15 Sample mean for comedy movies (x̄2) = 160 Since the population variances are assumed to be approximately equal, we can use the pooled standard deviation formula to calculate the sample standard deviation. Sample standard Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 82 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
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 randomly 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. Assume that the population variances are approximately equal. Box Office Revenues (Millions of Dollars) n x¯ s Drama 14 160 50 Comedy 19 120 10 Calculate a 99% 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.
Jon S.
A Hollywood studio believes that a movie which is considered a drama will draw a larger crowd on average than a movie which is a comedy. To test this theory, the studio randomly selects several movies which are classified as drama and several movies which are classified as comedy and determines the box office revenue for each movie. Without making any assumptions about the distribution, do the data substantiate the studio's belief that drama will draw a larger crowd on average than comedy? Use the Wilcoxon rank-sum test to analyze the results. Revenues (Millions of Dollars): Drama: 120, 150, 300, 280, 200, 260, 130, 130, 240, 210, 300, 220 Comedy: 220 Step 1 of 2: Find the value of the test statistic to test that dramas draw a larger crowd on average than comedy. Round your answer to two decimal places, if necessary. Step 2 of 2: Make the decision to reject or fail to reject the null hypothesis that drama will draw the same size crowd on average as comedy. Use α=0.025.
Shaiju T.
Hollywood believes that on average, a larger crowd will be drawn to movies considered to be dramas compared to movies considered to be comedies. To test this theory, a sample of movies considered to be comedies and a sample of movies considered to be dramas were taken to determine the mean box office revenue for each genre. The sample mean revenue for the dramas is $180 million, based on a sample of 25 movies, while the sample mean revenue for the comedies is $150 million, based on a sample of 30 movies. The population variances for dramas and comedies are 2,500 and 900, respectively. (All figures are in millions of dollars.) Do the data substantiate the studio's belief that dramas will draw a larger crowd on average compared to comedies? Test Ho: ̅̄d - ̅̄c ≤ 0 using a significance level of ̅̄.
Clarissa B.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD