Statistics 5/10/20

226 Bonus Review 4 – Chapters 13-15

For each of the following problems, conduct the appropriate analysis. In addition, for each word problem, conclude with a sentence that explains what the results MEAN.

1. The following shows the results of a two-factor ANOVA where there are 3 levels of factor A, 2 levels of factor B and n = 10 in each group. Fill in the table below.

	SS	Df	MS	F
Between	80
A
B				1.5
AXB	42
Within			3
Total

2. Meaghan wants to know if political affiliation is related to gender. So, she polls 20 men and 20 women to tell her whether they usually vote republican or democrat. The data follows. Is there a significant relationship between political affiliation and gender?

	Democrat	Republican
Female	13	7
Male	9	11

3. The following shows the results of a repeated-measures ANOVA where k=5 and n=20. Fill in the table below.

	SS	Df	MS	F
Between			15
Within
Subjects	24
Error
Total	464

4. In the general population, only 40% of people get their driver’s license by the time they turn 18. Elizabeth asks a sample of 50 people at what age they got their driver’s license and 12 of them report getting it by the time they turn 18. The rest of the people got it after they were already 18. Does this data depart significantly from what Elizabeth would expect based on the general population?

5. Daniel believes that kids who spend less time indoors will have better interpersonal skills. To test this, Daniel studies a sample of 20 kids in a third-grade class at his former primary school. He asks each kid how much time he or she spends indoors in a week (measured in hours) and also how many friends he or she has. Is there a significant negative relationship between time spent indoors and number of friends kids have? (HINT: we used this question in the bonus review for exam 1 so you probably already have some things computed.)

Time spent indoors (hours)	Number of friends
3 5 6 9 10 9 8 10 10 12 13 11 16 11 7 8 18 13 12 13	8 12 13 20 16 10 16 7 9 3 7 16 11 12 18 9 6 17 20 11

6. Ryan wants to know if weather affects mood. To that end, he asks the same 15 people to rate their moods at three different times – when it is raining, when it is sunny and when it is snowing. The data follows. Does weather significantly affect mood? SSsubjects = 100

Raining	Sunny	Snowing
M=5, s=1.5, n=15	M=8, s=1.1, n=15	M=8.4, s=3.1, n=15

7. Andrea wants to know if time of year affects mood. To that end, she asks the same 20 people to rate their moods at three different times – in April, in August and in December. Fill in the table below.

	SS	Df	MS	F
Between				5
Within	100
Subjects
Error
Total	120

8. Nathan is attending a conference where he is told that 30% of attendees will be students, 55% of attendees will be professors and 15% of attendees will be vendors. In one session at the conference, Nathan looks around him and notices that there are 14 students, 33 professors and 3 vendors in the room. Does this data depart significantly from what Nathan would expect based on what he was told?

9. Anna thinks there might be a relationship between hours spent commuting and final grades. So, she recruits a sample of 10 students and asks each one to note the number of hours they spend commuting within a week as well as their final grade in Anna’s class. The data follows. Is there a significant relationship between hours spent commuting and final grade?

Hours spent commuting per week	Final grade
6 9 7 3 2 4 5 5 3 6	75 72 77 82 90 80 81 88 79 81

10a. Kyle wants to know if time of day affects mood. To that end, he asks the same 5 people to rate their moods at three different times – in the morning, in the afternoon and in the evening. The data follows. Does time of day significantly affect mood?

Morning	Afternoon	Evening
6 7 8 6 5 M = 6.4, SS = 5.2	8 7 8 6 9 M = 7.6, SS = 5.2	7 8 6 5 7 M = 6.6, SS = 5.2

10b. Organize the results of this question in an ANOVA table and fill in the remaining blanks. You can ignore the MSwithin, MSsubjects, MStotal, Fwithin, Fsubjects, Ferror and Ftotal boxes.

11. Janice asks 30 people their preference between chocolate, vanilla and strawberry ice cream flavors. Of the 30 people asked, 15 pick chocolate, 9 pick vanilla and 6 pick strawberry. Does this data depart significantly from what would be expected by chance alone?

12. Scott wants to know if there is a relationship between attendance at a particular class and whether students pass or fail the final exam. He notes whether each of his 30 students were present or absent at the particular class of interest, and finds that 21 of the students were present. He then also notes whether each student passes or fails the final exam. Of the 21 students who were present at the class of interest, 18 of them passed the final exam. Of the 9 students who were not present, all of them passed the final exam. Is there a significant relationship between attendance at a particular class and whether students pass or fail the final exam?

13a. Jessica thinks that college major and year of study affect performance on a standardized math test. To determine if she is right, Jessica recruits a sample of 80 students for her experiment. Of her 80 students, Jessica recruits 20 students who are freshmen, 20 who are sophomores, 20 who are juniors and 20 who are seniors. Ten students from each year of study are Psychology majors and the other 10 students from each year of study are Math majors. Fill in the table below.

	SS	Df	MS	F
Between
College Major
Year of Study			20
CollMaj x YrStudy				5
Within	144
Total	234

13b. Is there a significant main effect of college major?

13c. Is there a significant main effect of year of study?

13d. Is there a significant interaction between college major and year of study?