Ch1 hw - optional hw problems for ch 1 PDF

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optional hw problems for ch 1...

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1. The data were collected from a statistics class. The column heads give the variable, and each of the rows represents a student in the class. How many variables are there? Male

Age

1 1 1 1

20 19 31 29

Eye Color Brown Hazel Brown Hazel

Shoe Size 12.5 11.5 11.5 11

There are

Height (inches) 60 64 65 72

Weight Number College Units Handedness (pounds) of Siblings This Term 160 4 13 Left 150 0 15 Right 160 2 16 Left 165 3 15 Right

variables.

(Type a whole number.)

ID: 1.2.1 2. The data were collected from a statistics class. The column head gives the variable, and each of the rows represents a student in the class. Complete parts a and b. Male

Age

1 0 0 1

21 31 30 29

Eye Shoe Color Size Hazel 8.5 Brown 9.5 Brown 6 Hazel 7.5

Height (inches) 70 71 71 65

Weight (pounds) 175 175 180 210

a. Is the variable Agenumerical or categorical? Explain. A. The variable is numerical because the values are categories. B. The variable is categoricalbecause the values are categories. C. The variable is categoricalbecause the values are numbers. D. The variable is numerical because the values are numbers. b. Is the variable Eye Color numerical or categorical? Explain. A. The variable is categoricalbecause the values are categories. B. The variable is numerical because the values are categories. C. The variable is numerical because the values are numbers. D. The variable is categoricalbecause the values are numbers.

ID: 1.2.3

Number College Units Handedness of Siblings This Term 4 5 Right 0 12 Right 1 7 Left 3 15 Right

3. The accompanying data were collected from a statistics class. The first row gives the variable, and each of the other rows represents a student in the class. What do the numbers 1 and 0 mean for the variable Female in the table (which is coded categorical data)? Often, it does not make sense, or is not even possible, to add a categorical variable. Does it make sense for Female? If so, what does the sum represent? 1

Click the icon to view the statistics class data.

The number 1 indicates that the subject (1) is (2)

is not

female. It (3)

female, while the number 0 indicates that the subject

does

make sense to add a categorical variable for Female, since it represents

females

a quality of the object of interest. The sum of the Female category represents the number of (4)

1: Statistics Class Data Female

(1)

is is not

Hair Ring Commute Distance (Miles) Color Size

Height (inches)

Number of Aunts

College Units Acquired

Living Situation

0 1 0 1

0 0 0 14

Blonde 10.5 Brown 9.5 Blonde 10 Brown 6

61 66 67 64

0 4 3 1

23 30 0 41

Dorm Dorm Dorm Commuter

1 0 0 0

17 0 0 0

Black Brown Black Brown

6 7.5 5 10

63 64 62 63

3 3 2 0

26 21 37 20

Dorm Commuter Commuter Commuter

1 0 1

21 13 0

Brown Brown Brown

11 7.5 8.5

63 63 61.5

1 4 3

39 40 44

Dorm Commuter Dorm

does

(4)

(2)

is not is

(3)

does not

classes people non-females females

ID: 1.2.7

surveyed.

4. A survey was done of men's and women's hands to see if the ring finger appeared longer than the index finger or not. Yes means the ring finger is longer, and No means the ring finger appears shorter or the same length as the index finger. The students in this survey were not told the theory that men are more likely to have a longer ring finger than women due to more testosterone. Complete parts (a) through (d) below.

Yes No

Men 37 9

Women 29 10

a. What percentage of the men said Yes? % of men said Yes. (Type an integer or decimal rounded to one decimal place as needed.) b. What percentage of the women said Yes? % of women said Yes. (Type an integer or decimal rounded to one decimal place as needed.) c. What percentage of the people who said Yes were men? % of the people who said Yes were men. (Type an integer or decimal rounded to one decimal place as needed.) d. If a large group of 350 men had the same rate of responses as the men in this sample, how many men of the350 would say yes? Of the 350 men,

would say yes.

(Round to the nearest whole number as needed.)

ID: 1.4.21

5. The first step in finding an association between gender and handedness from among the students in the accompanying table is to create a two-way table with these two variables. Make a two-way table with the labels Male and Female across the top and the labels Right and Left on the side, and then answer questions (a) through (f) using it. 2

Click the icon to view the data table.

a. Report how many students are in each of the four cells of the table by writing these values in your table. Refer to the spreadsheet given below to begin tallying. For each cell, make a tally mark using the capital letter I for each person who has both of the characteristics belonging to that cell. Type a 0 if there are no students with the given characteristics. The genders have been recorded without coding to make the tallying process a little easier. Put a check mark to the right of the table so you know how far you have gotten. The first four tally marks are given. Check to see that you have a total of 11 tally marks. 3

Click the icon to view the partial data table. Male

Right

I

Female II

Left

I

Next, summarize the table with numbers. Male

Female

Right Left b. Sum the numbers of students in each row and each column, and put these sums in your table. Put the total number of males in the location shown as TMale and put the total number of females at TFemale. Put the total number of subjects who are right-handed at TRight and the total number of those who are left-handed at TLeft. Note that the grand total (total number of people) is 11, as shown. Male

Female

Right

Total TRight =

Left Total

TLeft = TMale =

TFemale =

11

c. What percentage of the females are right-handed? % of the females are right-handed. (Type an integer or decimal rounded to one decimal place as needed.) d. What percentage of the right-handed students are female? % of the right-handed students are female. (Type an integer or decimal rounded to one decimal place as needed.) e. What percentage of the students are right-handed? % of the students are right-handed. (Type an integer or decimal rounded to one decimal place as needed.) f. If the percentage of right-handed females remained roughly the same and there were80 females, how many of them would be right-handed? Of the 80 females, of them would be right-handed. (Round to the nearest whole number as needed.)

2: Stats class data

Number of College Units Eye Color Shoe Size Height (inches) Weight (pounds) siblings This Term Hazel 8 62 135 0 8

Handedness 

Male

Age

1

32

0 0 0 1

31 29 31 32

Hazel Brown Hazel Hazel

10 10.5 10 6

70 72 66 71

195 135 200 125

1 2 1 6

16 11 15 7

Right Right Left Right

1 0 1 1

32 32 22 23

Hazel Hazel Brown Hazel

6.5 11 7 8.5

72 62 61 63

135 150 185 120

4 2 7 1

9 15 12 11

Left Left Right Left

1 0

22 22

Brown Hazel

6 10.5

66 62

190 145

5 2

8 13

Right Left

Right

3: Partial Data Table Gender

Handedness

Male Female

Right Right

Female Female Male Male

Right Left Right Left

Female Male Male Male

Left Right Left Right

Female

Left

Checked



ID: 1.4.27 6. Two sections of statistics are offered, the first at 8 a.m. and the second at 10 a.m. The 8 a.m. section has 25 women, and the 10 a.m. section has 15 women. A student claims this is evidence that women prefer earlier statistics classes than men do. What information is missing that might contradict this claim? Choose the best answer below. A. The professor may be female in one class and male in the other, which could affect the female students' class preference. B. The age and class standing of the students is unknown. Older female students may prefer later classes, so it may be only younger female students who prefer earlier classes. C. The percentage of female students in the two classes is unknown. There may be more females in the 8 a.m. because there are more students in the 8 a.m. class than the 10 a.m. class. This claim could be true only if the classes were the same size. D. No information is missing, this claim is true.

ID: 1.4.37

7. Patients with high blood pressure are asked to keep food diaries recording all items they eat for a one-week period. Researchers analyze the food diary data for trends. Indicate whether the study is an observational study or a controlled experiment. Choose the correct answer below. A. The study is a controlled experiment, because there is mention of random assignment. B. The study is a controlled experiment, because there is no mention of random assignment. C. The study is an observational study, because there is mention of random assignment. D. The study is an observational study, because there is no mention of random assignment.

ID: 1.5.39 8. Indicate whether the study is an observational study or a controlled experiment. A group of boys is randomly divided into two groups. One group watches violent cartoons for one hour, and the other group watches cartoons without violence for one hour. The boys are then observed to see how many violent actions they take in the next two hours, and the two groups are compared. The study is (1)

(1)

an observational study. a controlled experiment.

ID: 1.5.43 9. A group of educators want to determine how effective tutoring is in raising students' grades in a math class, so they arrange free tutoring for those who want it. Then they compare final exam grades for the group that took advantage of the tutoring and the group that did not. Suppose the group participating in the tutoring tended to receive higher grades on the exam. Does that show that the tutoring worked? If not, explain why not and suggest a confounding variable. Choose the correct answer below. A. Because this was an observational study, it only shows an association; it does not show that the tutoring worked. It could be that an insufficient number of students were studied to show that the tutoring worked. B. The study shows that the tutoring worked. C. Because this was an observational study, it only shows an association; it does not show that the tutoring worked. It could be that more motivated students attended the tutoring and that was what caused the higher grades.

ID: 1.5.47

10. In a 2017 study designed to investigate the effects of exercise on second-language learning, 40 subjects were randomly assigned to one of two conditions: an experimental group that engaged in simultaneous physical activity while learning the vocabulary in a second language and a control group that learned the vocabulary in a static learning environment. Researchers found that learning second-language vocabulary while engaged in physical activity led to higher performance than learning in a static environment. Complete parts (a) and (b) below. a. What features of a well-designed controlled experiment does this study have? Which features are missing? What features of a well-designed controlled experiment does this study have? Select all that apply. A. Double-blindedness B. Random assignment C. A large sample size D. Two-group division What features of a well-designed controlled experiment are missing from this study? Select all that apply. A. Random assignment B. A large sample size C. Double-blindedness D. Two-group division b. Assuming that the study was properly conducted, can we conclude that the physical activity while learning caused the higher performance in learning second-language vocabulary? Explain. The sample size of the study was (1)

(1)

small, large,

ID: 1.5.49

(2)

should should not

so we (2)

(3)

conclude that (3)

physical activity while learning did not cause higher performance. physical activity while learning caused higher performance.

11. An article in the journal BMC Medicine reported on a study designed to study the effect of diet on depression. Subjects suffering from moderate to severe depression were randomly assigned to one of two groups: a diet intervention group and a social support control group. The 33 subjects in the diet intervention group received counseling and support to adhere to a "ModiMedDiet," based primarily on a Mediterranean diet. The 34 subjects in the social support group participated in a "befriending" protocol, where trained personnel engaged in conversation and activities with participants. At the end of a 12-week period, 11 of the diet intervention group achieved remission from depression compared to 3 of the control group. Answer parts (a) through (c). 4

Click the icon to view the remission data.

a. Find and compare the sample percentage of remission for each group. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals rounded to one decimal place as needed.) A. Intervention remission %: %; Control remission %: %. The intervention remission percentage is greater than the control remission percentage. B. Intervention remission %: %; Control remission %: intervention remission percentage is equal to the control remission percentage.

%. The

C. Intervention remission %: %; Control remission %: intervention remission percentage is less than the control remission percentage.

%. The

b. Was this a controlled experiment or an observational study? Explain. A. The study is an observational study, because there is mention of random assignment. B. The study is a controlled experiment, because there is no mention of random assignment. C. The study is an observational study, because there is no mention of random assignment. D. The study is a controlled experiment, because there is mention of random assignment. c. Can we conclude that the diet caused a remission in depression? Why or why not? A. Yes, assuming that the results are significant, it would be reasonable to conclude causation because there is random assignment. B. No, we cannot conclude causation because the sample size was too large and there was blinding in the design. C. No, we cannot conclude causation because the sample size was fairly small and there was no blinding in the design. D. Yes, assuming that the results are significant, it would be reasonable to conclude causation because there is no random assignment.

4: Remission Data Remission No Remission

ID: 1.5.55

Diet (Intervention) Support (Control)  11 3 22

31...