## 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

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. Do the data substantiate the studio's belief that dramas will draw a larger crowd on average than comedies at α=0.01? Let dramas be Population 1 and comedies be Population 2. Assume that the population variances are approximately equal.
Box Office Revenues (Millions of Dollars)

``n    x¯    s``

Drama 15 180 60
Comedy 13 140 20

a. State the null and alternative hypotheses for the test. Fill in the blank below.
b. Compute the value of the test statistic. Round your answer to three decimal places.
c. Make the decision and state the conclusion in terms of the original question.

## A newspaper story claims that more houses are purchased by singles now than singles 5 years ago

A newspaper story claims that more houses are purchased by singles now than singles 5 years ago. To test this claim, two studies were conducted on the buying habits of singles over the past 5 years. In the first study, 500 house purchases in the current year were randomly selected and 150 of those were made by singles. In the second study, again 500 house purchases were randomly selected from 5 years ago and 117 of those were made by single people. Test the newspaper’s claim using a 0.05 level of significance. Is there sufficient evidence to support the newspaper’s claim? Let singles now be Population 1 and let singles 5
years ago be Population 2.
a. State the null and alternative hypotheses for the test. Fill in the blank below.
b. Compute the value of the test statistic. Round your answer to two decimal places.
c. Make the decision and state the conclusion in terms of the original question.

## Major television networks conducted a joint poll of viewers and asked them if they felt that beer and other alcoholic beverage commercials targeted te

Major television networks conducted a joint poll of viewers and asked them if they felt that beer and other alcoholic beverage commercials targeted teenagers and young adults (those under 21 years old). The results of the survey are as follows. Based on the data, can the networks conclude that the percentage of viewers who believe beer and alcoholic beverage commercials target teenagers and young adults is significantly higher in the over 30 age group than in the 30 or younger age group at α=0.01? Let the 30 or younger age group be Population 1 and let the older than 30 age group be Population 2.

Age Group Number Surveyed Number of "Yes" Responses
30 or Younger 1000 484
Older than 30 1000 526

a. State the null and alternative hypotheses for the test. Fill in the blank below.
b. Compute the value of the test statistic. Round your answer to two decimal places.
c. Make the decision and state the conclusion in terms of the original question.
d.

## An auto dealer would like to determine if there is a difference in the braking distance

An auto dealer would like to determine if there is a difference in the braking distance (the number of feet required to go from 60mph to 0mph) of two different models of a high-end sedan. Six drivers are randomly selected and asked to drive both models and brake once they have reached exactly 60mph. The distance required to come to a complete halt is then measured in feet. The results of the test are as follows. Can the auto dealer conclude that there is a significant difference in the braking distances of the two models? Use α=0.01. Let the braking distances of Model A represent Population 1 and the braking distances of Model B represent Population 2.
Braking Distance of High-End Sedans (Feet)
Driver 1 2 3 4 5 6
Model A 156 149 148 151 150 154
Model B 158 153 149 152 150 155
a. State the null and alternative hypotheses for the test. Fill in the blank below.
b. Compute the value of the test statistic. Round your answer to three decimal places.
c. Make the decision and state the conclusion in terms of the original question.
d.

## An SAT prep course claims to improve the test score of students

An SAT prep course claims to improve the test score of students. The table below shows the scores for seven students the first two times they took the verbal SAT. Before taking the SAT for the second time, each student took a course to try to improve his or her verbal SAT scores. Do these results support the claim that the SAT prep course improves the students' verbal SAT scores?
Let d=(verbal SAT scores prior to taking the prep course)−(verbal SAT scores after taking the prep course)
. Use a significance level of α=0.05 for the test. Assume that the verbal SAT scores are normally distributed for the population of students both before and after taking the SAT prep course.
Student Score on first SAT Score on second SAT
1 380 420
2 440 530
3 470 530
4 490 550
5 440 460
6 420 490
7 410 430

a. State the null and alternative hypotheses for the test.
b. Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.
c. Compute the value of the test statistic. Round your answer to three decimal places.
d. Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places.
e. Make the decision for the hypothesis test.