Chapter 1 work

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Chapter 1 work

True/False
Indicate whether the statement is true or false.

A hypothesis is a statement that is always true.

The following statement is a hypothesis. Girls watch more TV than boys.

The following hypothesis is true. The Moon orbits Earth once every year.

Every student in the class has an equal chance to be picked in a random sample.

The following set of ordered pairs has a linear relationship:
(0, 0), (1, 1), (2, 4), (3, 9), (4, 16)

Modified True/False
Indicate whether the statement is true or false. If false, change the identified word or phrase to make the statement true.

It is possible to compare different sized samples by using percents or fractions. _________________________

Time is the dependent variable in a distance-time graph. _________________________

A downward straight line in a distance-time graph of a car’s movement means that the car is losing speed. _________________________

A non-linear graph is produced in a distance-time graph when a person changes speed. _________________________

10.

Primary data can be obtained from an encyclopedia. _________________________

Multiple Choice
Identify the choice that best completes the statement or answers the question.

11.

Which of the following is a primary source of data?

a.	an article in a magazine
b.	a database
c.	conducting an experiment to test the effectiveness of a new medication
d.	an entry from an on-line encyclopedia

12.

Which of the following is not an example of random sampling?

a.	Use a random number generator to pick 10% of the players in each division of a hockey league.
b.	Use a randomly generated number between 1 and 10 to pick a name on a list, and then select every 8th person on the list.
c.	Ask every 10th person entering a mall for an opinion on government spending on health care.
d.	Write names on slips of paper, and then pick the names out of a hat, making sure the pieces of paper are well mixed.

13.

The table shows the height of a bean plant in the first week after it germinated. Predict the height of the bean plant on the eighth day.

Day	1	2	3	4	5	6	7
Height (cm)	0.9	1.8	2.6	3.6	4.4	5.5	6.1

a.	6.7	c.	7.5
b.	7.1	d.	8.0

14.

Before a fishing derby began, a group of friends made the predictions below. This table shows the numbers of fish caught. Whose prediction was correct?

Number of Fish Caught	0	1	2	3	4	5	6	7	8
Caught by This Many Entrants	18	14	13	8	4	4	2	0	1

a.	Heather predicted that most entrants would not catch any fish.
b.	George predicted that most entrants would catch only 1 fish.
c.	Alun predicted that most entrants would catch 5 or more fish.
d.	Hans predicted that most entrants would catch less than 3 fish.

15.

Students in a grade 9 phys-ed class were surveyed about how often they exercise in a week.

Time	Frequency
Every day	10
Every other day	6
Only on weekends	14

If there are 1000 students in the school, how many do you expect exercise every day?

a.	268	c.	396
b.	333	d.	400

Short Answer

16.

This table shows the numbers of days absent from mathematics class and the math marks for 15 students.

Number of Days Absent	Math Mark (%)
2	82
0	75
10	48
6	62
1	76
23	35
13	42
2	96
1	54
3	73
7	65
0	79
10	60
16	43
1	84

a) Identify the independent variable and the dependent variable. Explain your reasoning.
b) Make a scatter plot of the data.
c) Describe the relationship between a student’s marks and attendance.
d) Are there any outliers? If so, explain how they differ from the rest of the data.

17.

The table lists a skateboarder’s speed on reaching the bottom of a steep ramp after starting from different heights on the ramp.

Initial Height (m)	1.5	2.5	3.0	3.5	4.5	5.0	5.5	6.0
Speed (m/s)	3.9	4.9	5.4	5.9	6.8	7.3	7.9	8.5

a) Identify the dependent and independent variables.
b) Make a scatterplot of the data.
c) Describe the relationship between the variables.

18.

In a discussion with her friends, Kristen argued that the Internet was used mostly for e-mail, rather than for general browsing or entertainment. She discovered this table showing the percent of households that used the Internet for each activity in 2004.

Activity	%
Electronic banking	14.7
E-mail	37.4
Financial information	18.5
Formal education/training	19.0
General browsing	36.2
Medical or health information	22.9
Obtaining and saving music	17.8
Playing games	18.2
Travel information/arrangements	21.9
Viewing the news	20.4

a) State Kristen’s hypothesis.
b) Did Kristen use primary or secondary data?
c) Do the data support Kristen’s hypothesis?

19.

Tom’s movements after he left his house are shown on this distance-time graph. Describe his movements.

20.

The data in this table show the daily average times, in hours, of watching TV and the mathematics marks for 10 students.

Time (h)	1	6	3	2	10	0	2	5	2	12
Mark (%)	83	53	71	73	90	81	68	51	70	40

a) What is the independent variable?
b) Make a scatter plot of the data.
c) Identify any outliers.
d) Describe the relationship between the students’ daily average time watching TV and their mathematics marks.

21.

A skydiver jumps from an airplane. The distance fallen and time taken are recorded in the table.

Time (s)	Distance (m)
0	0
1	5
2	19
3	42
4	74
5	115

a) Draw a scatter plot of the relation.
b) Classify the relation as linear or non-linear. Explain your choice.
c) How far will the skydiver have fallen in 3.5 s?

22.

State a hypothesis about a relationship between the variables in each pair. Then, state the opposite hypothesis.
a) the amount of electricity used in a house and the temperature during winter
b) a pet dog’s mass and how much food it eats each day
c) the size of an animal and its lifespan

23.

Explain why each sample may not provide accurate information about its population.
a) You survey of 12 of your friends to determine the music that is best liked by Canadians.
b) A survey of senior citizens is used to find the most popular hobby among Ontarians.
c) To find the ratio of foreign to North American cars in Ontario, a survey is conducted of cars in the parking lot of the Ford Motor Company in Oakville, Ontario.

24.

Classify the sampling technique used in each survey as simple random, systematic random, stratified random, or non-random sampling.
a) The principal selects people in the cafeteria to interview about the quality of cafeteria food.
b) A computer is programmed to randomly select 100 names from a club’s membership list.
c) Students are selected at random, with the number of students in each age group selected proportional to the size of the age group.
d) To select 100 people who can buy concert tickets, the ticket agent randomly selects one wristband number and then every 10th number after that.

25.

The table shows Carmen’s heart rate after climbing stairs.

Number of Stairs Climbed	10	20	30	40	50
Heart Rate (beats/min)	80	85	92	100	115

a) Draw a scatter plot of the data in the table.
b) What is the independent variable?
c) Describe any pattern(s) that you see in the scatter plot.
d) Approximately what is Carmen’s heart rate after climbing 25 stairs?
e) About how many stairs had Carmen climbed when her heart rate was 95 beats/min?

Problem

26.

The table shows the levels of education of Canadian workers from 1996 to 2005.

Year	1996	1997	1998	1999	2000	2001	2002	2003	2004	2005
High School (thousands)	3000	3100	3050	3090	3200	3190	3150	3100	3050	2980
College/ Trade (thousands)	2450	2600	2710	2920	3010	3100	3150	3240	3330	3450
University (thousands)	4500	4800	5000	5040	5070	5300	5450	5550	5700	5850

a) State a hypothesis about the relationship between the numbers of Canadian workers and their levels of education.
b) On the same grid, make scatter plots for the three sets of data.
c) Use the scatter plots to compare the trends in the data.
d) Do the data support your hypothesis? Give reasons for your response.

27.

The table shows the winning throws in the discus in the Olympic Games since 1956.

Year	Men’s Distance (m)	Women’s Distance (m)
1956	56.36	53.69
1960	59.18	55.10
1964	61.00	57.27
1968	64.78	58.28
1972	64.40	66.62
1976	67.50	69.00
1980	66.64	69.96
1984	66.60	65.36
1988	68.82	72.30
1992	65.12	70.06
1996	69.39	69.65
2000	69.30	68.40
2004	69.89	67.02

a) Graph both sets of data.
b) Use your graphs to compare any trends in the men’s and in the women’s data.
c) Identify any outliers. What may account for such outliers? Explain whether you should discount these outliers.
d) Use the data and the graphs to predict the winning distances for the men’s and women’s discus in the 2012 Olympic Games. Give reasons for your estimates.

28.

Linda trained for a triathlon by swimming from a beach to a floating dock. The table shows how far she was from the beach at certain times.

Time (min)	0	5	10	15	20	25	30	35
Distance (m)	0	200	390	610	610	400	200	0

a) How far is it from the beach to the floating dock?
b) During which 5-min period did Linda swim fastest?
c) Make a distance-time graph for Linda’s swim.
d) Estimate when Linda was 300 m from the beach. Justify your response.
e) Use the distance-time graph to write a summary of Linda’s swim.

29.

The data in the table show the average distance of each planet from the Sun and its orbiting speed.

Planet	Distance From Sun (millions of kilometres)	Orbiting Speed (thousands of kilometres per hour)
Mercury	58	173
Venus	108	126
Earth	150	107
Mars	228	87
Jupiter	778	47
Saturn	1427	35
Uranus	2871	25
Neptune	4498	20
Pluto	5906	17

a) Make a scatter plot of the data with distance from the Sun as the independent variable.
b) Use the scatter plot to describe the relationship (if any) between the variables.
c) Is the relationship linear or non-linear? Explain.

30.

The table shows the mean number of children born to women in Canada between the ages of 15 and 49 over the years 1950 to 2000.

Year	1950	1960	1970	1980	1990	2000
Birth Rate	3.46	3.90	2.34	1.74	1.86	1.49

a) Graph the data.
b) Describe any trends that you can find in the data.
c) What birth rate would you predict for 2010? Explain your prediction.