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exam_1.docMath 213: Applied Statistics Exam 1 Spring 2011
Name ____________________ Grade: ______ / 100
This part of the exam includes Multiple Choice and True/False questions worth 3 points each. Circle the correct answer. There is only one correct answer for each problem.
1. Which of the following statements are true?
I) A parameter is a number that describes the population.
II) Different samples provide different values for the sample statistic.
III) Sample statistic is a number that is usually unknown.
A) I
B) I and II
C) I, II and III
2. _________ Statistics is a branch of Statistics that consists of methods used to summarize and organize data obtained from a sample.
A) Descriptive
B) Inferential
C) Experimental
3. An auto analyst is conducting a satisfaction survey. He divides the list of new car buyers into Ford buyers, GM buyers, Honda buyers, and Toyota buyers and then randomly selects a sample from each group. This is an example of:
A) Systematic Sampling
B) Stratified Sampling
C) Cluster Sampling
4. A magazine editor designs a survey to better serve the interests of the magazine’s readers. Some of the questions about the respondent include the respondent’s
I) Race
II) Gender
III) Age
Which of these variables are categorical?
A) I
B) I and II
C) I, II, and III
5. Twenty first graders were asked which color they liked best - red, green, or blue. Their responses appear below.
red, green, green, blue, red, blue, red, red, blue, red red, blue, red, red, blue, red, blue, green, green, red
Which of the following tables correctly summarizes responses from the first graders?
|
Table I |
|
|
Table II |
|
|
Category |
Frequency |
|
Category |
Relative Frequency |
|
Blue |
6 |
|
Blue |
60% |
|
Green |
4 |
|
Green |
40% |
|
Red |
10 |
|
Red |
10% |
A) Table I
B) Table II
C) Both Table I and Table II
The histogram below shows the number of televisions owned by each family on a city block. Use the histogram to answer Question 6 and Question 7.
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
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6. Describe the shape of the distribution.
A) Symmetric
B) Skewed to the left
C) Skewed to the right
7. How many families are represented by the histogram?
A) 10
B) 20
C) 26
8. The median annual salary of a registered nurse in the United States is $62,089. That means
A) The average of all registered nurses salaries is $62,089
B) Half of the registered nurses make $62,089
C) Half of the registered nurses make less than $62,089
9. For the three cases below, choose the one for which the range for Data Set A is bigger than the range for Data Set B.
A) Data Set A: 2, 5, 8, 1
Data Set B: 1, 5, 7, 9
B) Data Set A: 2, 8, 3, 1
Data Set B: 3, 6, 2, 1
C) Data Set A: 4, 5, 2, 1
Data Set B: 9, 8, 5, 6
10.The __________ is interpreted as the average distance from any data point in the data set to the mean.
A) Z-Score
B) Standard Deviation
C) Sample Variance
11. A small standard deviation implies that the data values are clustered close to the mean.
A) True
B) False
12. Your LSAT score represents the 75th percentile. That means
A) You got 75% of the questions correct.
B) 75% of the test scores were less than your score.
C) 75% of the test scores were greater than your score.
13. A data value has a z-score of 0. That means
A) The data value is an outlier.
B) The data value is equal to the mean.
C) The data value is equal to the standard deviation.
14. Two data sets with the same mean will always have the same standard deviation.
A) True
B) False
This part of the exam includes calculation problems. Please show all relevant work. When necessary, round to two decimal places.
15. Every year, about 50,000 runners compete in the Peachtree Road Race in Atlanta Georgia. They run 10 kilometers (a little over 6 miles). Mary ran in 2008 with the finishing time of 65 minutes. That year, the average finishing time of all runners was 55 minutes, with a standard deviation of 10 minutes. Mary’s sister, Shannon ran in 2010 with a finishing time of 50 minutes. In 2010, the average finishing time of all runners was 65 minutes with the standard deviation of 12 minutes.
A) Calculate the z-score for Mary’s finishing time. (7 points)
B) Calculate the z-score for Shannon’s finishing time. (7 points)
C) Relative to the groups that they ran with, which of the girls had a better finishing time? Why? (6 points)
16. Find the standard deviation for the data set given below: (10 points)
34 21 25 79 75
17. The heights of 1,000 males follow a bell-shape distribution with the mean of 170 cm and the standard deviation of 8 cm.
A) What percentage of males will be taller than the average height of 170 cm? (7 points)
B) What percentage of males will have a height between 154 cm and 186 cm? ( 7 points)
This part of the exam includes open ended questions.
18. Describe the difference between a population and a sample. ( 7 points)
19. Define what a z-score of a data value is. Give one reason for why you would want to convert a data value into a z-score. (7 points)
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