STAT 1000 Assignment 2016

Question
Question 1 (5 points)

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(a) The manager of an ice cream store at Grand Beach would like to study the relationship between the temperature and the amount of ice cream the store sells. The temperature X (in degrees Celsius) and the total ice cream sales Y (in \$) for the first six Saturdays of the summer are shown below:

Date

Temp

Sales

June 22

22.7

269

June 29

32.4

504

July 6

26.4

350

July 13

19.8

323

July 20

28

462

July 27

29.6

574

From the data, it can be calculated that,, and

What is the value of the correlation coefficient, r? Show all your work

(b) Given the strong positive correlation between the variables, can we say that the temperature increasing causes ice cream sales to increase? Explain.

Question 2 (6 points)

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We would like to determine how a person’s cholesterol level can be predicted by his or her fat consumption. The average daily fat consumption (in mg) and the cholesterol levels for a sample of eight individuals are shown below:

Individual

1

2

3

4

5

6

7

8

Fat Consumption

6577

5803

8908

10006

7700

9346

4224

7650

Cholesterol Level

180

201

211

270

202

250

190

221

From these data, it can be calculated that and.

*Give all answers to four decimal places.

(a) What is the equation of the least squares regression line for predicting cholesterol level from fat consumption?

(b) What proportion of the variation in a person’s cholesterol level can be predicted by his or her fat consumption?

(c) What is the predicted cholesterol level for an individual with an average daily fat consumption of 6461 mg?

(d) What is the value of the residual for Individual 2?

(e) Suppose we had instead measured fat consumption in grams (1 gram = 1000 milligrams). What would have been the correlation between fat consumption and cholesterol level?

Question 2 options:

We would like to see how a city’s location can help predict its weather. The latitude (in degrees north of the equator) and average January temperature (in degrees Celsius) are shown below for a sample of cities in the northern hemisphere:

City

Latitude

Avg. January
Temperature

Paris, France

48.5

3

Manila, Philippines

14.4

26

Tel Aviv, Israel

32.1

13

Mexico City, Mexico

19.3

14

45.5

-9

44.5

2

Dublin, Ireland

53.2

5

Bogota, Colombia

4.4

17

New York City, USA

40.4

1

Lagos, Nigeria

6.3

27

Delhi, India

28.4

15

Riga, Latvia

56.6

-4

Caracas, Venezuela

10.3

22

Athens, Greece

37.6

10

Kiev, Ukraine

50.3

-5

Hong Kong, China

22.2

17

(a) Using JMP, create a scatterplot of this data. Create two columns, one titled Latitude and the other titled Temperature and enter the data. Select Analyze > Fit Y by X, click Latitude, then X, Factor, and click Temperature, then Y, Response, then OK. Under the red arrow, select Fit Line. This will add the least squares regression line to the scatterplot. You do not need to attach the scatterplot.

Interpret the meaning of the slope of the least squares regression line for predicting temperature from latitude.

(b) What is the value of the correlation between latitude and temperature?

(c) Winnipeg has a latitude 49.9 degrees north of the equator. What is the predicted average January temperature for Winnipeg?

(d) Reykjavik, Iceland has a latitude 64.1 degrees north of the equator. What is the predicted average January temperature for Reykjavik?

(e) Is one of your predictions in (c) and (d) more reliable than the other? Explain.

(f) What is the value of the residual for New York City? What does the sign of the residual tell us?

Question 4 (6 points)

A golfer would like to conduct an experiment to determine how the brand of club he uses, the brand of ball he uses, and the height of tee affect the distance of his shots. (A golf tee is a small wooden or plastic peg placed in the ground, upon which the ball is placed prior to the first shot on a hole). The golfer will examine three different brands of golf clubs (Titleist, Callaway or Nike), two brands of golf balls (Pinnacle or Maxfli) and two different tee heights (low or high). The golfer will take ten shots using each of the factor level combinations, and the distance (in yards) for each shot will be recorded.

(a) What type of experiment is this?

(b) Identify the factor(s) in this experiment.

(c) Identify the factor levels in this experiment.

(d) Identify the treatments in this experiment.

(e) Identify the response variable in this experiment.

(f) Suppose that responses for one of the treatment groups are significantly more favourable than for other treatment groups. Can we say that the treatment is likely the cause? Explain.

Question 5 (9 points)

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A group of psychologists would like to study the effect of puzzle size and background music on the speed with which an individual is able to complete a jigsaw puzzle. A total of 84 people volunteer to participate in the study. Each individual will be randomly assigned to do either a 200 or 500 piece jigsaw puzzle with either classical, rock or pop music playing in the background. The psychologists anticipate that men and women may respond to the treatments differently, so the experiment is conducted separately for the 36 male volunteers and the 48 female volunteers.

(a) What type of experiment is this?

Identify the following in this experiment:

(b) experimental units

(c) response variable

(d) factors

(e) factor levels

(f) treatments

(g) Is there a blocking variable in this experiment? If so, what is it?

(h) How is the principle of control used in this experiment?

(i) How is the principle of replication used in this experiment?

Question 5 options:

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Question 6 (3 points)

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We would like to conduct an experiment to determine how alcohol impairs an individual’s ability to drive. Drivers will be asked to drive through a closed course sober, as well as after consuming three alcoholic beverages. The number of cones knocked over will be compared. There are 15 drivers and two days available for the study.

Explain how a matched pairs experiment should be conducted to compare the performance of drivers depending on whether they are sober or after consuming alcohol. Be sure to explain the role of randomization, and why it is important in this experiment.

The NHLPA is a union representing all National Hockey League players. The union is conducting a survey to gauge players’ opinions about a proposed change in the league’s salary structure.

For each of the following proposed sampling schemes, identify (i) the type of sample that is obtained and (ii) any bias in the way the sample is chosen.

*Note: When conducting a survey by phone, by mail or even in person, there is always the possibility that someone will refuse to respond. This cannot be avoided, even using proper sampling techniques. For part (ii) of each question, only describe the potential bias (if any) introduced by the way the sample is selected.

(a) A random sample of five players from each of the league’s 30 teams is selected. These selected players are contacted by a union representative. Random digit tabel

(b) The survey is sent to all players in the league. Players are asked to respond by email.Simple random sample

(c) The survey is distributed to players attending an NHLPA meeting in New York.

(d) A random sample of seven NHL teams is selected. Ten players from each of these ten teams are randomly selected and are contacted by telephone to respond to the survey.

(e) Two hundred players are randomly selected from a list of all NHL players. Union representatives administer the survey in person to each of the selected players.

(f) The survey is posted on the NHLPA’s private website. Players are invited to email their comments to a union representative.

Question 8 (6 points)

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The 15 teams in the National Basketball Association’s Western Conference are numbered and are shown in the table below:

01

Mavericks

06

Nuggets

11

Warriors

02

Rockets

07

Timberwolves

12

Clippers

03

Grizzlies

08

Thunder

13

Lakers

04

Pelicans

09

Trailblazers

14

Suns

05

Spurs

10

Jazz

15

Kings

Use the following string of random digits to select a simple random sample of six teams. Which six teams are included in your sample?

Note: you will receive 6 out of 6 points if your answer is completely correct; otherwise, you will receive 0 out of 6 points.

63091 40735 86970 14092 71026 55201 72698 11305

Question 8 options:

A)

Warriors

B)

Trailblazers

C)

Clippers

D)

Grizzlies

E)

Jazz

F)

Rockets

G)

Timberwolves

H)

Kings

I)

Suns

J)

Spurs

K)

Lakers

L)

Mavericks

M)

Thunder

N)

Pelicans

O)

Nuggets

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