Two Independent Samples Checkpoint

You are analyzing data for a research project. You have a two-sided two-sample t-test with the following hypotheses being tested: H0: μ1 − μ2 = 0 Ha: μ1 − μ2 ≠ 0 Which of the following results for the confidence interval provides enough evidence to reject the null hypothesis? 95% confidence interval: (−3.853, −0.943) 95% confidence interval: (−0.285, 1.345)

95% confidence interval: (−3.853, −0.943)

The owner of a test prep company was interested in whether students who took the company's face to face test prep class did better on the GRE (a standardized test required for admission to many graduate programs) than students who followed the test prep company's live online program. The live online test prep class met in an online classroom with live video instruction for the same number of hours as the face to face class. In which situation could the test prep company use the two-sample t-test for comparing two population means? A. The students take part of their GRE test prep course online and the remaining part in the face to face method. The test prep company asks the students which they liked better. The company wants to determine if the majority prefer the online class. B. The test prep company randomly divides the students into two groups. One of the groups receives the face to face test prep class and the other group receives the live online test prep class. After completing their test prep course, each student takes the GRE and the test prep company compares the test scores of the two groups. C. The test prep company gives each student a pretest. Then each student completes the live online test prep class. Afterwards, each student takes a posttest. The test prep company wants to compare the pretest and posttest GRE scores for each student to see whether the data will show an improvement.

B

Do college students who are in a fraternity or sorority attend more parties than college students who are not affiliated with a fraternity or sorority? A statistics class randomly selected 50 students who were in a fraternity or sorority and 50 students who were not affiliated with a fraternity or sorority and asked them to report how many parties they had attended in the past month. If µ1 and µ2 represent the number of parties attended by the fraternity and sorority members (µ1) and the unaffiliated students (µ2), respectively, which of the following is the appropriate pair of hypotheses in this case? H0: μ1 − μ2 = 0 Ha: μ1 − μ2 < 0 H0: μ1 = μ2 Ha: μ1 < μ2 H0: μ1 − μ2 > 0 Ha: μ1 − μ2 = 0 H0: μ1 = μ2 Ha: μ1 > μ2

H0: μ1 = μ2 Ha: μ1 > μ2

Do college students who are in a fraternity or sorority attend more parties than college students who are not affiliated with a fraternity or sorority? A statistics class randomly selected 50 students who were in a fraternity or sorority and 50 students who were not affiliated with a fraternity or sorority and asked them to report how many parties they had attended in the past month. The following hypotheses were tested: H0: µ1 = µ2 Ha: μ1 > μ2 Analyses were run. The following is the (edited) output for the test: Which of the following is an appropriate conclusion based on the output? The data provide sufficient evidence to reject the H0; thus, we cannot conclude that the mean number of parties attended by fraternity and sorority members is higher than those attended by unaffiliated students. The data provide sufficient evidence to reject H0; thus, we can conclude that the mean number of parties attended by fraternity and sorority members is higher than those attended by unaffiliated students. The data do not provide sufficient evidence to reject the H0; thus, we can conclude that the mean number of parties attended by fraternity and sorority members is higher than those attended by unaffiliated students. The data do not provide sufficient evidence to reject H0; thus, we cannot conclude that the mean number of parties attended by fraternity and sorority members is higher than those attended by unaffiliated students.

The data provide sufficient evidence to reject H0; thus, we can conclude that the mean number of parties attended by fraternity and sorority members is higher than those attended by unaffiliated students.

A journalist is interested in whether there is a significant difference in the salary offered to electrical engineering and chemical engineering graduates at the University of Texas at Austin. She reviews the statistics for starting annual salaries for 2013-2014 and finds the following: The test statistic is t = 2.4693, with a p-value of 0.0142. Which of the following is an appropriate conclusion? The samples provide evidence that there is a statistically significant difference between the starting salary of chemical engineering and electrical engineering graduates at the University of Texas at Austin for 2013-2014. The samples do not provide statistically significant evidence that there is a difference in starting salaries of chemical engineering and electrical engineering graduates at the University of Texas at Austin for 2013-2014. We cannot use the t-test in this case because the variables (starting salary of engineering graduates) may not be normally distributed.

The samples provide evidence that there is a statistically significant difference between the starting salary of chemical engineering and electrical engineering graduates at the University of Texas at Austin for 2013-2014.

A teacher is experimenting with a new computer-based instruction and conducts a study to test its effectiveness. In which situation could the teacher use the two-sample t-test for comparing two population means? The teacher randomly divides the class into two groups. One of the groups receives computer-based instruction and the other group receives traditional instruction without computers. After instruction, each student takes a test and the teacher wants to compare the test scores of the two groups. The teacher uses a combination of traditional methods and computer-based instruction. She asks students which they liked better. She wants to determine if the majority prefer the computer-based instruction. The teacher gives each student in the class a pretest. Then she teaches a lesson using a computer program. Afterwards, she gives each student a post-test. The teacher wants to compare test scores for each student to see whether the data will show an improvement.

The teacher randomly divides the class into two groups. One of the groups receives computer-based instruction and the other group receives traditional instruction without computers. After instruction, each student takes a test and the teacher wants to compare the test scores of the two groups.

In a study of the impact of smoking on birth weight, researchers analyze birth weights (in grams) for babies born to 189 women who gave birth in 1989 at a hospital in Massachusetts. In the group, 74 of the women were categorized as "smokers" and 115 as "nonsmokers." The difference in the two sample mean birth weights (nonsmokers minus smokers) is 281.7 grams and the 95% confidence interval is (76.5, 486.9) Which gives the best interpretation of what we can conclude about the impact of smoking on birth weight? This study does not suggest that there is a difference in mean birth weights when we compare smokers to nonsmokers. We are 95% confident that on average, smoking causes lower birth weights of between 76.5 grams to 486.9 grams. When smokers are compared to nonsmokers, we are 95% confident that the mean weight of babies of nonsmokers is between 76.5 grams to 486.9 grams more than the mean weight of babies of smokers. There is a 95% chance that if a woman smokes during pregnancy her baby will weigh between 76.5 grams to 486.9 grams less than if she did not smoke.

When smokers are compared to nonsmokers, we are 95% confident that the mean weight of babies of nonsmokers is between 76.5 grams to 486.9 grams more than the mean weight of babies of smokers.