Math153 DD1                                            Name: _______________________

Test1A, 3/02REV        SEE INSTRUCTOR TO DETERMINE HOW YOUR TEST   WILL BE DIFFERENT.

(5 points)

1)  Match the term to its explanation, example or definition.  Place the best choice (letter) in the blank.

 

a) parameter                             ___ a measure of variability

b) categorical                            ___ data such as height of an individual

c) measurement                        ___ data such as gender (female/male)

d) median                                 ___ a quantity from a population such as s

e) variance                                ___ a type of average

 

(12 points)

2)  An ice-skating contestant was given the following scores by 10 judges.

   2,   9,   9,   9,   2,   2,   2,   9,   2,   9

 

a)  Find the mean, median, mode, and 10 % trimmed mean.

mean = _________

 

median = __________

 

mode(s) = __________

 

10% trimmed mean = _____________

 

b)  Which average do you think is the best and why? _______ You must briefly explain your answer.

 

 

 

 

 

 

(10 points)

3)  The following distances are ski jumping points for a random sample of five contestants in an Olympic game (Men’s K120 Individual Final).  Use your calculator to find the sample mean and the sample standard deviation. Write down all places your calculator displays.

 

225.6,   226.2,   247.2,   245.6,   197.4

 

Mean =  ________________________

 

Sample standard deviation = ____________________________

 

 

 (4 points)

4)  The graph below depicts a dramatic reduction in the price of a tire.  Why is it misleading?  Explain fully.

 


 

 


(4 points    Select the best answer.)

5)  In order to find out how its employees felt about higher student fees imposed by the Board of Trustees, a university divided employees into three categories: staff, faculty, and student employees.  A random sample was selected from each group; they were telephoned and asked for their opinions.  This type of sampling procedure produces a

 

a)      cluster sample

b)      convenience sample

c)      simple random sample

d)      stratified sample

e)      systematic sample

 

 

 

 

 

(4 points)

6)  A set of test scores has a mean of 80, a range of 18, and a variance of 4.

What is the standard deviation? _______  You must explain your answer or show your work.

 

 

 

 

 

 

 

 

 

 

(9 points)

7)  The boxplots below describe the grades of three statistics classes. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


a)       Which class has the highest median grade (1, 2, or 3)? ____

 

b)       Which class shows the most variation in the grades ( 1, 2, or 3)? ____

 

c)       For class 1, what percent of the students scored less than 80? ______

 

 

-CONTINUED-

(20 points)

8)  A study attempts to determine if the number of dollars spent each week for lottery tickets is related to the household income for a person.  A small random sample of lottery players is taken.  x is the annual household income in units of $1000 ( 20 means $20,000.)  y is the number of dollars spent each week on lottery tickets.

 

Household income

Dollars spent per week on the lottery

10

30

20

30

20

20

30

10

40

4

 

a)     

Draw a scatterplot below of dollars spent versus household income.

b)      Find the equation of the regression line.  Round off numbers to two decimal places.

_____________________________________________________

 

c)      What is the slope of this regression line? ___________

d)      Explain the meaning of the slope of this regression line.  To obtain full credit, you must be specific.

 

 

 

 

 

 

 

 

e) What is the correlation coefficient, r? ________

 

f)  What is the predicted number of dollars spent per week on the lottery when the household income is $15,000?  Show all work below. _________

 

 

 

 

 

 

 

 (20 points)

9)  Weights of Type 1 dogs are normally distributed with mean = 60 lbs. and standard deviation = 5 lbs.  Weights of Type 2 dogs are normally distributed with mean = 40 lbs. and standard deviation = 5 lbs.

You may draw the appropriate diagrams below.

 

 

 

 

 

 

 

 

 

a)      95% of the weights of Type 1 dogs lie between _______ and ________.

 

b)      What percent of Type 1 dogs weigh less than 50 lbs.? ______

 

c)      A Type 2 dog with a weight of 45 lbs. is in what percentile? ________

 

d)      What is the z-score for a Type 1 dog weighing 55 lbs.? ______

 

e)      Is a Type 2 dog weighing 60 lbs. unusual? ______

You must explain for credit.

 

 

 

 

 

 

 

OMIT for TEST1  (5 points)

10)  Check which numbers could be probabilities.

 

____ 1/3          ____ -2/3               ____ 2.3          ___ 0.7            ____ 0

 

 

OMIT for TEST1 (8 points)

11)  One regular, fair die is thrown.  Define the events A and B below.

 

a) A is the event of getting a number which is at least 5. P(A) = _________

 

 

b) B is the event of getting a number less than 2.                  P(B) = _________

 

 

d)      Find P(A or B) = _______

 

Answers

1. e,c,b,a,d

2. a) mean=5.5, median=5.5, modes=2 and 9, 10% trimmed mean=5.5

b)  mode if multiple answers are acceptable, because the data are bimodal.

3)  Mean=228.4, Sample standard deviation = s= 20.14298885

4)  The change in price is $.50 from 1998 to 2002, a very small amount.

5) d

6) 2 (=square root of 4)

7)a) 3   b) 2      c) 50%

8)b)  or y = -.95x + 41.69    c)  -.95

d) As household income increases by1 unit or $1000, the average predicted amount spent on lottery tickets in a week decreases by $.95.

e)  -.93

f)  = -.95(15)+41.69 = $27.44

9)  a)  50 and 70          b)  2.5%           c)  84th       d) –1          e) Yes,

the z-score = (60-40)/5 = 4

10) FOR TEST2,  ½, 0.7, 0

11) FOR TEST2, a)  2/6 or 1/3      b) 1/6   c) 3/6 or 1/2