Mathematics

NAME:  _________________________________________________     Worksheet #1

Due ________­­­­________________

 

1. For each of the following variables, decide whether it is qualitative (L) or quantitative (N).

______   a.   number of wheels on a vehicle                       ______   c.   a person’s favorite color

______   b.   county a person lives in                                ______   d.   distance a person drives to work

————————————————————————————————————————————————–

2. For each of the following quantitative variables, decide whether it is discrete (D) or continuous (C).

______   a.   number of marbles in a jar                              ______   c.   weight of a baby at birth

______   b.   number of hours a phone battery lasts         ______   d.   number of TV’s in a household

————————————————————————————————————————————————–

3. A shipment of 2000 tire pressure gauges arrives at an automotive company warehouse. Fifty of the

tire gauges are randomly selected from various parts of the shipment and the percent of those that

are defective is determined.  If this percentage is greater than 5%, the shipment is sent back.

 

Which of the following is the population of interest for this example?

1. all tire pressure gauges                                         the 2000 tire gauges in the shipment
2. the 50 randomly selected tire gauges                   5% of the tire gauges in the shipment

 

Which of the following is the sample for this example?

1. all tire pressure gauges   the 2000 tire gauges in the shipment
2. the 50 randomly selected tire gauges   5% of the tire gauges in the shipment

 

If 4 of the 50 randomly selected tire gauges are found to be defective, what percentage is that?  Show work.

1. 4%                                      8%
2. 5%                               d.  0.08%

 

The percentage in the previous question is a  _____________ .

1. parameter                           statistic

 

Would the shipment be returned?

1. Yes, because more than 5% of the 50 tire pressure gauges were defective.
2. No, because less than 5% of the 50 tire pressure gauges were defective.
3. Unable to be determined because they didn’t check the whole shipment.

————————————————————————————————————————————————–

4. Decide in each of the following cases whether it is an example of an observational study (O)

or an experiment (E).

______     a.   Does attending an SAT preparation course improve scores?  A comparison is done of

the math SAT scores between students who attend a 6 week preparation course and

those who do not.

 

______    b.   Is there a significant difference in the SAT scores of students who are right-handed as

opposed to those who are left-handed?  A comparison is done of the math SAT scores

between students who are right-handed and those who are left-handed.

 

5. From the numbered list of South Carolina counties given below, you must select a sample of 6 of them

using the string of random digits shown below.   Move across that row two digits at a time (since 46 is a

two-digit number) clearly showing your work.  Your answer should include the names and numbers of the

counties selected for your sample, in the order you choose them.

 

1.      Abbeville         13.   Chesterfield     25.   Hampton          36.   Newberry
2. Aiken                               14.   Clarendon        26.   Horry                               37.   Oconee
3. Allendale         15.   Colleton           27.   Jasper              38.   Orangeburg
4. Anderson         16.   Darlington        28.   Kershaw           39.   Pickens
5. Bamberg          17.   Dillon                               29.   Lancaster         40.   Richland
6. Barnwell          18.   Dorchester       30.   Laurens            41.   Saluda
7. Beaufort           19.   Edgefield          31.   Lee                  42.   Spartanburg
8. Berkeley          20.   Fairfield           32.   Lexington         43.   Sumter
9. Calhoun           21.   Florence          33.   McCormick       44.   Union
10. Charleston 22.   Georgetown     34.   Marion             45.   Williamsburg
11. Cherokee 23.   Greenville        35.   Marlboro          46.   York
12. Chester 24.   Greenwood

 

 

1 8 6 2 0     3 5 8 4 9     2 7 3 9 4     4 8 2 3 6     3 3 5 0 9     5 2 9 7 8

 

1.                      name

 

1. _____ ____________________________________
2. _____ ____________________________________
3. _____ ____________________________________
4. _____ ____________________________________
5. _____ ____________________________________
6. _____ ____________________________________

—————————————————————————————————————————————

 

6. IN AN EXPERIMENT, THERE ARE FOUR CHARACTERISTICS THAT SHOULD BE PRESENT.

EACH IS LISTED BELOW.   MATCH THEM WITH THEIR DEFINITIONS.

 

1. control                   b.   randomization                   c.   replication             d.   double-blindness

 

______   How are the subjects assigned to their treatment groups?  This assignment must be truly random,

something akin to drawing names out of a hat.

 

______   There must be a group with whom the experimenter can compare the group that is receiving the

treatment of interest.  This comparison group usually receives the ‘old, tried-and-true’ treatment

or receives no treatment at all in the form of a placebo.

 

______   In an experiment with human subjects, neither the subjects nor the experimenter should know

who receives what treatment until the end of the experiment.  This usually requires the use of

an impartial third party.

 

______   If the experiment were repeated under similar conditions, would the results be similar?

This is ensured by either repeating the experiment to compare the results or by using a

large sample the first time in order to get reliable results.

 

7. Below are the recorded speeds of cars on a road with a 50 mph speed limit:

 

42        55        51        48        37        45        46        54

61        43        58        51        40        49        53        50

48        47        44        54        52        59        45        52

 

X  =   ________________________________________________________

 

1. Construct a split stem-and-leaf diagram           b.   Complete the frequency distribution for the speeds.

to organize the data.                                                Use six classes with 35 as the lower limit of the

first class, and use a class width of 5.

speed          frequency

35-39

40-44

 

 

 

 

 

 

————————————————————————————————————————————————–

1. Construct a histogram using the frequency distribution in part b.         d.   What is the overall shape of

Label the axes.                                                                                                    the distribution?

____   symmetric

____   skewed left

____   skewed right?

 

 

 

 

 

 

 

 

 

 

_____________________________________________________________

 

 

 

 

 

8. Label the graphs below with one of the following: symmetric (S), skewed right (R), skewed left (L).

 

 

 

______                                                    ______                                                ______

 

9. The eye colors of forty people are given below.

 

L = blue                      R = brown                    G = green                    H = hazel

 

L     G     G     R     G     R     L     G     R     H     L     R     R     H     G     L     R     L     L     G

R     G     L     R      R     L     G     R     L      R     R     L     R     G     L     G     R     L     R     R

 

1. Complete the following chart.                                          Construct a frequency bar graph.  Label axes.

 

 

color      frequency        relative frequency

 

 

 

 

 

 

 

  

______________________________________

 

 

 

————————————————————————————————————————————————–

 

1. Which eye color occurred most frequently?    ____________________________

 

 

 

10. A pie chart showing the breakdown of political party affiliation of the registered voters in a small town is

given below.  Use the pie chart to answer the following questions.  Show all work!

 

D = Democrat         R = Republican                        I = Independent           L = Libertarian

 

 

 

D

• What percent of the voters in this town is Independent?

 

45%

 

 

6%

L

———————————————————————————————

R

• What is the degree measure of the angle for ‘Republican’?

 

32%

I

 

 

 

———————————————————————————————

1. If there were 3640 voters in this town, how many are Democrat?