Question

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
Ha: ?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.

Answer 1

The independent samples t-statistic is calculated to be approximately 3.22, using the given mean scores, standard deviations, and sample sizes for comedies and thrillers.

Step-by-step explanation:

The producer is conducting a hypothesis test to compare the population means of two independent samples, where the population standard deviations are unknown and are not assumed to be equal. To calculate the test statistic (t), we use the formula for the independent samples t-test:

t = (X₁ - X₂) / √((s₁²/n₁) + (s₂²/n₂))

In this case, the sample mean score for comedies (X₁) is 85.5 with a sample standard deviation (s₁) of 15.6 and sample size (n₁) of 52. The sample mean score for thrillers (X₂) is 77.6 with a sample standard deviation (s₂) of 6.5 and sample size (n₂) of 32.

Plugging these values into the formula, we get:

t = (85.5 - 77.6) / √((15.6²/52) + (6.5²/32))

t = 7.9 / √((15.6²/52) + (6.5²/32))

t = 7.9 / √((243.36/52) + (42.25/32))

t = 7.9 / √((4.68) + (1.32))

t = 7.9 / √(6)

t = 7.9 / 2.45

t = 3.22

Therefore, the calculated t-value is approximately 3.22.