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Test1 Key(STP 226) FormA
1. An instructor gives a quiz with 3 questions, each worth 1 point. The distribution
of the class scores is as follows:
SCORE
RELATIVE FREQUENCY
0
0.40
1
0.30
2
0.20
3
0.10
If there were 30 people in the class, how many scored 2 or above?
Answ : 30% of 30, 0.3*30=9
2. The appropriate notation for a sample mean is
a) 
b) x c)  d) s e) z
f) none of these
Answ: B
3.Consider the following stem & leaf diagram and compute the median
of the data it represents.
0|59759
Data : Hair Mercury Content of
1|38877994134
Seychelles Fishermen
2|1647291629
3|422098135
Stems: tens
4|21
5|8
leaves: ones
6|48
Answer: Median = (obs20+obs21)/2= (22+24)/2=23
You needed to order only leaf labeled 2: 1 1 2 2 4 6 6 7 9 9
4. Compute sample standard deviation of the following data set, use the
definition, show work.
2, 2, 4, -1, 0, 5
Answ: x =2 s2 =1/5[ (2-2)2 + (2-2)2+ (4-2)2 + (-1-2)2 + (0-2)2 + (5-2)2 ] = 5.2
s = 2.28
5. The distribution of some data is given by the graph below. The mean of this data
is greater than the median. True or false?
Answ : false, mean < median
6. As reported in News by the Department of Agriculture the mean weekly food cost
for a couple with two children 6-11 years old is $95.40 with a standard
deviation of $17.20. Assume that the distribution has a "bell shape"
Fill in the blanks:
99.7 % of such couples have a weekly cost between $ 43.8 and $ 147
(95.4+or- 3(17.2)) Empirical Rule
7. Following are several variables. Which if any yield qualitative data?
a) height b) age
c) number of siblings d) place of birth
e) weight
f) sex
g) religion
h) high-school class rank
Answ: D, F, G
8. Find the mode of the following data set
3, 12, 5, 12, 4, 8, 12, 7, 10, 4
Answ: 12
9. The more variation there is in the data set, the smaller its standard deviation.
True or false?
Answ: false, more variation, larger st. dev.
10. The population z-score for a certain data value is equal to -2.5. This data value
is smaller than the population mean. True or false?
Answ: True, it is smaller z=(x-)/
11. A sample of a certain type of snake in Arizona produced the following data for
the lengths (in inches) of 22 snakes:
16, 22, 24, 28, 29, 30, 31, 31, 32, 33, 34, 35, 36, 37, 38, 40, 45, 48, 50, 51, 58,78
a) (6 points) Give the 5 number summary of the data (MIN, MAX, Median, Q1
and Q3) and make a box plot.
Answ: Min=16, Q1=30, Q2=34.5, Q3=45, use units 10-80.
(or if you use formula from the book: Q1=29.75, Q2=34.5, Q3 = 45.75)
Box plot looks about like the one below, be careful & use true scale.
b) (4 points) Compute IQR and use it to check for outliers in this
data set. List the potential outliers.
Answ: IQR=15, upper limit=30-1.5(15)=7.5, Lower limit= 45+1.5(15)=67.5
78 is a potential outlier.
Limits change slightly if you use Q1= 29.75 and Q3=45.75, but 78 still is an outlier.
12. Consider the following data:
x
-2
-1
0
1
2
=0
y
2
2
3
4
4
=15
x2
4
1
0
1
4
=10
xy
-4
-2
0
4
8
=6
a) (6 points) Determine the least squares regression line in the form
y  b0  b1x . You may use your calculator.
Answ:
Sxy=6 - (0)(15)/5=6
Sxx=10-(0)(0)/5=10
b1=6/10=0.6
b0=15/5-0.6(0/5)=3
b) (4points)Use the least-squares line from part a) to predict y for x = 0.7 and for
x = 13. Are your predictions reasonable in both cases? Explain why or why not.
Answ: for x=.7 predicted y=3+.6(.7)=3.42,
for x=13 predicted y=10.8
Prediction for x=13 is called extrapolation and it does not give reasonable results,
since x=13 is outside of data range.