# Material from Ch1-5

**STP 226Place Label Here**

**EXAM #1 (100 points)**

**Material from Ch1-5**

Instructor:

**Honor Statement:**

**I have neither given nor received information regarding this exam, and I will not do so until all exams have been graded and returned.**

Signed ______

DIRECTIONS:

**This is a closed book examination. The formula card from the book is attached at the end of the test. **

**There are 17 problems. Provide complete and well-organized answers. **

**Show your work! **

**1. [ 5 points] An instructor gives a quiz with 3 questions, each worth 1 point. The distribution of the class scores is as follows:**

** SCORE RELATIVE FREQUENCY**

00.40

10.30

20.20

30.10

**If there were 30 people in the class, how many scored 2 or above?**

**2. [ 5 points] Consider the following stem & leaf diagram and compute the median of the data it represents. **

**0 | 5 9 7 5 9Data : Hair Mercury Content of **

**1 | 3 8 8 7 7 9 9 4 1 3 4Seychelles Fishermen**

**2 | 1 6 4 7 2 9 1 6 2 9**

**3 | 4 2 2 0 9 8 1 3 5 Stems: tens**

4 | 2 1

**5 | 8leaves: ones**

6 | 4 8

3. [ 6points] Compute sample standard deviation of the following data set by hand, use the definition, show work.

2, 2, 4, -1, 0, 5

4. [ 5 points] The more variation there is in the data set, the smaller its standard deviation.

True or false?

5. [ 5 points] The blood pressure readings for a random sample of 100 patients between ages 25 and 40 of some hospital are presented by the histogram below. Use the histogram to identify the overall shape of the distribution of the sample as (roughly):

bell-shaped

uniform

right skewed

left skewed

bimodal

(select one only)

Relative Frequency

Systolic Blood Pressure (mm Hg)

Circle the letter of the best choice in problems 6 and 7

6. [ 5 points]To select a sample of size 10 from a list of 500 students, every 50th student is selected, starting with the 3rd student. Identify the type of sampling used here.

a.Simple random samplingb.Cluster sampling

c.Systematic random samplingd.Stratified sampling

7.[ 5 points] A pollster wants to interview a sample of 500 voters from a community of 10,000 voters. He uses a computer to generate 500 random numbers between 1 and 10,000 and then interviews the voters corresponding to those numbers.

Assume that he list of voters numbered 1-10,000 is available.

Identify the type of sampling used in this example.

a.Stratified samplingb.Simple random sampling

- Systematic random samplingd.Cluster sampling

8. [ 6 points] The distribution of some data is given by the graph below. The mean of this data is smaller than the median. True or false? Explain.

Use the following information in problems 9 and 10:

As reported in News by the Department of Agriculture the mean weekly food cost for an American couple with two children 6-11 years old is $95.40 with a standard deviation $17.20.

9. [ 6 points] Fill in the blanks:

Almost all of American couples with two children 6-11 years old couples have a weekly food cost between

$ ______and $ ______.

10. [ 6 points] One random couple was selected and z-score was computed for their weekly food cost . That z –score, z = -1.5.

Is their weekly food cost smaller or larger than the population mean of $95.4?

Explain.

11. [ 5 points] Following are several variables. Which if any yield quantitative data?

a) height b) age c) number of siblings d) place of birth

e) weight f) sex g) religion h) Blood type

12. [ 5 points] Find the mode of the following data set

3, 12, 5, 12, 4, 8, 12, 7, 10, 4

13. [ 6 points] Toss two balanced dice, one red, one green.

What is the probability that the sum of both dice is 6 or 11?

14. [ 6 points] A frequency distribution for the number of siblings of 45 students in one of the STP 226 classes is given in the table below:

Number of siblings / 0 1 2 3 4 5 6 7Number of students (frequency) / 7 6 12 8 5 4 2 1

For a student selected at random from that class, let

A= event that student has at most 3 siblings

B= event that student has at least 2 siblings

Compute P(A&B).

Are events A , B mutually exclusive? Clearly explain why or why not?

Use the following data in problems 15 and 16:

A sample of a certain type of snake in Arizona produced the following data for

the lengths (in inches) of 22 snakes:

22, 16, 24, 28, 29, 31, 30, 31, 32, 33, 34, 51, 36, 38, 37, 40, 45, 48, 78, 35, 58, 50

15. [ 6 points] Give the 5 number summary of the data (MIN, MAX, Median, Q1

and Q3) and make a box plot. Use proper scale.

16. [ 6 points] Compute Interquartile range, IQR, and use it to check for outliers in this data set, show work. List the potential outliers. If there are no potential outliers, state it.

17. [ 12points] The EPA 1980 49-state (all except California) combined mileage rating and engine volume are shown below for 9 standard-transmission, four-cylinder, gasoline-fueled, subcompact cars. The engine sizes are in total cubic inches of cylinder volume.

Car / x = Cylinder Volume (inch3) / y = mpgVW Rabbit

Datsun 210

Chevette

Dodge Omni

Mazda 626

Oldsmobile Starfire

Mercury Capri

Toyota Celica

Datsun 810 / 97

85

98

105

120

151

140

134

146 / 24

29

26

24

24

22

23

23

21

a) Obtain the equation of the least squares regression line for the data . You may use your calculator. Give units of a slope.

b)Explain carefully what is the criterion satisfied by the “least squares regression line”.

c) Use the least-squares line to predict the mean miles per gallon for

a subcompact automobile that has 105 cubic inches of engine volume and compute the error you made by using the regression line.

g) Compute what percent of variation in miles per gallon (y ) is explained by

the regression model? Does it mean that the regression line fits well?