1

Select one answer.

10 points

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?

1. 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.
2. 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.
3. 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.

Question 2

Select one answer.

10 points

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 20132014 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?

1. 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 20132014.
2. 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 20132014.
3. We cannot use the t-test in this case because the variables (starting salary of engineering graduates) may not be normally distributed.

Question 3

Select one answer.

10 points

Breastfeeding burns up to 500 calories per day, so does that mean that women who breastfeed their infants will lose more weight than women who formula feed their infants? A group of researchers studied the amount of weight lost after giving birth by mothers who breastfed their infants and mothers who chose formula feeding. They randomly chose 29 breastfeeding mothers and 21 formula feeding mothers. The researchers recorded how much weight each group lost at 12 months after childbirth. The amount of weight lost was found to be normally distributed. The difference in the mean amount of weight lost for the two samples (breastfeeding vs. formula feeding) is 2.0 kg and the 95% confidence interval is (1.05, 4.19).

Which statement gives the best interpretation of what we can conclude about the impact of breastfeeding on the amount of weight lost after childbirth?

1. When breastfeeding mothers are compared to formula feeding mothers, we are 95% confident that the mean amount of weight lost 12 months after childbirth is between 1.05 kg and 4.19kg more than the mean amount of weight lost by formula feeding mothers.
2. This study does not suggest that there is a difference in mean amount of weight lost after childbirth when we compare breastfeeding mothers to formula feeding mothers.
3. There is a 95% chance that if a woman breastfeeds her baby that she will lose an extra 1.05 kg to 4.19 kg than if she used formula to feed her baby.
4. We are 95% confident that on average, breastfeeding causes an extra weight loss of 1.05 kg to 4.19 kg.

Question 4

Select one answer.

10 points

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 1 and 2 represent the number of parties attended by the fraternity and sorority members (1) and the unaffiliated students (2), respectively, which of the following is the appropriate pair of hypotheses in this case?

1. H₀: _{1 2}= 0

   H_a: _{1 2}< 0

2. H₀: ₁= ₂

   H_a: ₁< ₂

3. H₀: _{1 2}> 0

   H_a: _{1 2}= 0

4. H₀: ₁= ₂

   H_a: ₁> ₂

Question 5

Select one answer.

10 points

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: ₁= ₂

H_a: ₁> ₂

Analyses were run. The following is the (edited) output for the test:

Which of the following is an appropriate conclusion based on the output?

1. 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.
2. 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.
3. 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.
4. 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.

Question 6

Select one answer.

10 points

You are analyzing data for a research project. You have a two-sided two-sample t-test with the following hypotheses being tested:

H₀: _{1 2}= 0

H_a: _{1 2} 0

Which of the following results for the confidence interval doesnotprovide enough evidence to reject the null hypothesis?

1. 95% confidence interval: (4.223, 1.989)
2. 95% confidence interval: (2.945, 0.983)