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Elementary Statistics: Skills Practice Exam 1- Lessons 1, 2, 12

Module by: Susan Dean, Dr. Barbara Illowsky

Questions 1 – 4 use the following table and shows the lengths (in minutes) of 64 international phone calls using a prepaid calling card.

Length of call (minutes) Frequency Relative frequency Cum. Relative Freq.
4 25 0.3906  
14 15    
24 10 0.1563  
34 9 0.1406  
44 4 0.0625  
54 1 0.0156 1.00

Exercise 1

The histogram of this data looks to be:

  • A. Skewed right
  • B. Skewed left
  • C. Symmetrical

Solution 1

A

Exercise 2

Which of the following box plots most accurately displays the data?

  • A. A box with line segments extending to the right and the left. The box is divided in to a large rectangle on the left and a square on the right.
  • B. A box divided into two equal size rectangles with a line segment extending to the right.
  • C. A box with a line segment extending to the left and the box is divided into two rectangles. The rectangle to the left is larger than the one on the right.
  • D. A box divided into two equal size rectangles with a line extending to the right and the left.

Solution 2

B

Exercise 3

What percent of telephone calls were more than 24 minutes?

  • A. 15.63%
  • B. 21.88%
  • C. 62.5%
  • D. 78.13%

Solution 3

B

Exercise 4

Find the 80th percentile.

  • A. 14
  • B. 24
  • C. 34
  • D. 70

Solution 4

C

Exercise 5

What can be said about a set of data when its standard deviation is small (but not zero)?

  • A. The data are far apart.
  • B. All of the data have the same value.
  • C. The mean of the data can never be zero.
  • D. The data are close together.

Solution 5

D

Questions 6 and 7, refer to the following: A sample of students was taken to determine pulse rate. The data is shown:

Pulse rate-beats per minute 54 58 65 68 72 76 80 90 98
Frequency (# of Students) 1 3 6 8 5 3 8 4 2

Exercise 6

Find the median and mode(s).

  • A. 72, 68 and 80
  • B. 72 and 80
  • C. 76 and 68
  • D. 76, 68 and 80

Solution 6

A

Exercise 7

Out of the entire college population of 24,000 students, approximately what percent of students are expected to have a pulse rate of 65?

  • A. 6
  • B. 40
  • C. 9
  • D. 15

Solution 7

D

For questions 8 and 9, refer to the following: By determining the average number of people in a car using the "Diamond" Carpool Lane, the California Highway Patrol is trying to decide if the number of people in a car using the "Diamond" Carpool Lane should be increased from 2 to 3.

Exercise 8

The average number of people per car for all cars using the "Diamond" Carpool Lane is called the:

  • A. parameter
  • B. data
  • C. variable
  • D. statistic

Solution 8

D

Exercise 9

The number of people in 1 car is called the:

  • A. parameter
  • B. data
  • C. variable
  • D. statistic

Solution 9

C

Exercise 10

I toss a fair coin a large number of times. Assuming the tosses are independent, which of the following is true?

  • A. Once the number of flips is large enough, the number of heads will always be exactly half of the total number of tosses. For example, after 10,000 tosses I should have exactly 5,000 heads.
  • B. The proportion of heads will be about 1/2 and this proportion will tend to get closer to 1/2 as the number of tosses increases.
  • C. As the number of tosses increases, any long run of heads will be balanced by a corresponding run of tails so that the overall proportion of heads is exactly 1/2.
  • D. All of the above.

Solution 10

B

Questions 11 - 13, refer to the following: A sample of twenty people went on a cruise to Alaska. Their two-week weight gain is shown below (a weight loss is shown by a negative number.)

Weight Gain Frequency
-2 4
0 5
2 8
5 2
9 1

Exercise 11

The middle 50% of the data is between ________ and _________.

  • A. 0 and 2
  • B. 0 and 9
  • C. 2 and 9
  • D. 2 and 2

Solution 11

A

Exercise 12

Find the average weight gain (in pounds).

  • A. 1.35
  • B. 2.74
  • C. 2
  • D. There is not enough information.

Solution 12

A

Exercise 13

What weight gain is 3 standard deviations above the mean (in pounds)?

  • A. 4.05
  • B. 8.19
  • C. 9.57
  • D. There is not enough information

Solution 13

A

For questions 14 - 19, use the following information: Kim, a personal trainer, was interested in whether or not there was a linear relationship between the number of visits her clients made to the gym each week and the average amount of time her clients exercised per visit. She took the following data.

Client 1 2 3 4 5 6
Number of visits per week 1 3 4 2 3 5
Average time spent exercising per visit (hours) 2 1.5 1 2 2 0.30

Exercise 14

The line that best fits the data is:

  • A. ŷ = -0.44 + 2.62 x ŷ=-0.44+2.62x
  • B. ŷ = 0.44 + 2.62 x ŷ=0.44+2.62x
  • C. ŷ = 2.62 + 0.44 x ŷ=2.62+0.44x
  • D. ŷ = 2.62 - 0.44 x ŷ=2.62-0.44x

Solution 14

A

Exercise 15

Is the correlation coefficient significant?

  • A. Yes
  • B. No
  • C. It might be.
  • D. Not enough information is given.

Solution 15

A

Exercise 16

Using the best fit line, estimate the average time spent exercising per visit for 4 visits per week.

  • A. 2 hours
  • B. 0.86 hours
  • C. 1 hour
  • D. 10.04 hours

Solution 16

B

Exercise 17

Kim used the best fit line to estimate the average time spent exercising per visit for her client Toby who visited the gym 7 times per week. Does the least squares line give an accurate estimate?

  • A. Yes
  • B. No
  • C. Maybe
  • D. Not enough information is given.

Solution 17

B

Exercise 18

If the correlation coefficient is –1, which answer is correct?

  • A. The slope of the best fit line is positive.
  • B. The slope of the best fit line is –1.
  • C. The data fit exactly on a line with positive slope.
  • D. The data fit exactly on a line with negative slope.

Solution 18

D

Exercise 19

A scatter plot shows:

  • A. the direction and strength of a relationship between the independent and dependent variables.
  • B. that there is a linear relationship between the independent and dependent variables.
  • C. how you can predict the dependent variable knowing the independent variable.
  • D. nothing. The line of best fit is what is important.

Solution 19

A

Exercise 20

Suppose we are interested in the average grade on the first math 10 test taken by all students at De Anza during the spring 2002 quarter. We randomly choose 3 students from each of the spring 2002 Math 10 classes as our sample. This sampling technique is

  • A. systematic
  • B. cluster
  • C. stratified
  • D. convenience

Solution 20

B

Exercise 21

Tracy works at a local indoor soccer arena. He is interested in the proportion of people entering the area who spend money in the arena store. One night while he is working, Tracy counts the first 20 people who buy goods in the arena store.

  • A. systematic
  • B. cluster
  • C. stratified
  • D. convenience

Solution 21

D

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