is my answer I have correct A movie producer has been handed

(is my answer I have correct)

A movie producer has been handed two scripts. One is a wacky comedy going by the name of \"Poindexter Joins The Army\" and the other is a psychological thriller known as \"The Deconstructionist\". The producer does not know which film to invest in. He is interested in knowing if there is any difference between people\'s enjoyment of comedies and people\'s enjoyment of thrillers. He decides to conduct a hypothesis test comparing these.

He collects a random sample of 51 people and asks them to rate how much they enjoy comedies with a score out of 100. He also collects a random sample of 38 people and asks them to rate thrillers with a score out of 100.

The sample mean for comedies is 77.5 and the sample standard deviation is 18.0. The sample mean for thrillers is 69.6 and the sample standard deviation is 6.9. The producer is going to conduct a test comparing the population mean score for comedies (?₁) to the population mean score for thrillers (?₂). The following hypotheses will be used:

H₀: ?₁ = ?₂

H_a: ?₁ ? ?₂

The producer believes that there is more variety in people\'s appreciation of comedies, and so he assumes that the two population standard deviations are not equal in this situation.

Calculate the test statistic (t) for this test. Give your answer to 3 decimal places.

t = 2.865

Solution

Here is what I solved before, please modify the figures as per your question. Please let me know if you have further questions. Ifthis helps then kindly rate 5-stars.

A movie producer has been handed two scripts. One is a wacky comedy going by the name of \"Poindexter Joins The Army\" and the other is a psychological thriller known as \"The Deconstructionist\". The producer does not know which film to invest in. He is interested in knowing if there is any difference between people\'s enjoyment of comedies and people\'s enjoyment of thrillers. He decides to conduct a hypothesis test comparing these.

He collects a random sample of 52 people and asks them to rate how much they enjoy comedies with a score out of 100. He also collects a random sample of 32 people and asks them to rate thrillers with a score out of 100.

The sample mean for comedies is 85.5 and the sample standard deviation is 15.6. The sample mean for thrillers is 77.6 and the sample standard deviation is 6.5. The producer is going to conduct a test comparing the population mean score for comedies (?₁) to the population mean score for thrillers (?₂). The following hypotheses will be used:

H₀: ?₁ = ?₂

H_a: ?₁ ? ?₂

The producer believes that there is more variety in people\'s appreciation of comedies, and so he assumes that the two population standard deviations are not equal in this situation.

Calculate the test statistic (t) for this test. Give your answer to 3 decimal places.

t =

Answer

n1= 52: n2 = 32

x bar = 85.5% y bar = 77.6%

sigma 1 = 15.6 and sigma 2 = 6.5

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Difference between means:
M1-M2=85.5-77.6=7.9
sd=21.09; se=2.4496
95% CI of difference:
3.099 <7.9< 12.701

t statistic = 3.225

p value =0.002

As p value is very small reject null hypothesis.

There is difference between the means of people seeing comedies and thrills.

Set up hypotheses as

H0: mu1 = mu2

Ha: mu1 >mu2

One tailed test

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Variances are not equal.