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STAT 200 6389 Introduction to Statistics

This is an open-book exam. You may refer to your text and other course materials as you work on the

exam, and you may use a calculator. You must complete the exam individually. Neither collaboration nor

consultation with others is allowed. It is a violation of the UMGC Academic Dishonesty and Plagiarism policy

to use unauthorized materials or work from others.

Answer all 10 questions. Make sure your answers are as complete as possible. Show all of your supporting

work and reasoning. Answers that come straight from calculators, programs or software packages without

any explanation will not be accepted. If you need to use technology (for example, Excel, online or handheld

calculators, statistical packages) to aid in your calculation, you must cite the sources and explain how you

get the results.

Record your answers and work on the separate answer sheet provided.

This exam has 10 questions: 10% for each question.

You must include the Honor Pledge on the title page of your submitted mid-term exam.

Exams submitted without the Honor Pledge will not be accepted.

1. Define variables with examples.

2. State which type of measurement scale each represents, and then which center measures can be

use for the variable?

a.

b.

c.

d.

3.

You collect data on the height of plants using a new fertilizer.

You collect data on the cars that people drive in Campbelltown, Australia.

You collect data on the temperature at different locations in Antarctica.

You collect data on the first, second, and third winner in a beer competition.

Choose the best answer. Justify for full credit.

(a) A study was conducted at a local college to analyze the average GPA of students graduated

from UMGC in 2016. 100 students graduated from UMUC in 2016 were randomly selected, and

the average GPA for the group is 3.5. The value 3.5 is a

(i) statistic

(ii) parameter

(iii) cannot be determined

(b) The hotel ratings are usually on a scale from 0 star to 5 stars. The level of this measurement is

(i) interval

(ii) nominal

(iii) ordinal

(iv) ratio

(c) On the day of the last presidential election, UMUC News Club organized an exit poll in which

specific polling stations were randomly selected and all voters were surveyed as they left those

polling stations. This type of sampling is called:

(i) cluster

(ii) convenience

(iii) systematic

(iv) stratified

4. The frequency distribution below shows the distribution for IQ scores for a random sample of 1000

adults. (Show all work. Just the answer, without supporting work, will receive no credit.)

IQ Scores Frequency Cumulative Relative

Frequency

50 – 69 23

70 – 89 249

90 -109 0.722

110 – 129

130 – 149 25

Total 1000

(a) Complete the frequency table with frequency and cumulative relative frequency. Express the

cumulative relative frequency to three decimal places.

(b) What percentage of the adults in this sample has an IQ score of at least 110?

(c) Which of the following IQ score groups does the median of this distribution belong to? 70 Ã¢â‚¬â€œ 89,

90 Ã¢â‚¬â€œ 109, or 110 Ã¢â‚¬â€œ 129? Why?

5. The five-number summary below shows the grade distribution of a STAT 200 quiz for a sample of 100

students.

Answer each question based on the given information, and explain your answer in each case.

(a) What is the range in the grade distribution?

(b) Which of the following score bands has the most students?

(i) 30 Ã¢â‚¬â€œ 50

(ii) 50 Ã¢â‚¬â€œ 70

(iii) 70 Ã¢â‚¬â€œ 90

(Iv) Cannot be determined.

(c) How many students in the sample are in the score band between 70 and 100?

6. Explain with example: When you use pie chart, and bar chart?

7. In Connecticut households use gas, fuel oil, or electricity as a heating source. Table #1 shows the

percentage of households that use one of these as their principle heating sources (“Electricity usage,”

2013), (“Fuel oil usage,” 2013), (“Gas usage,” 2013). Create a bar chart and pie chart of this data. State

any findings you see from the graphs.

Table #1: Data of Household Heating Sources

Heating Source

Electricity

Fuel Oil

Gas

Other

Percentage

15.3%

46.3%

35.6%

2.8%

8. Suppose you have an experiment where you flip a coin three times. You then count the number of

heads.

a.) State the random variable.

b.) Write the probability distribution for the number of heads.

c.) Draw a histogram for the number of heads.

d.) Find the mean number of heads.

e.) Find the variance for the number of heads.

f.) Find the standard deviation for the number of heads.

g.) Find the probability of having two or more number of heads.

h.) Is it unusual to flip two heads?

9. Find the z-score corresponding to the given area. Remember, z is distributed as the standard normal

distribution with mean of m = 0 and standard deviation s = 1.

a.) The area to the left of z is 15%.

b.) The area to the right of z is 65%.

c.) The area to the left of z is 10%.

d.) The area to the right of z is 5%.

e.) The area between -z and z is 95%. (Hint draw a picture and figure out the area to the left of

the -z .)

f.) The area between -z and z is 99%.

10.

The median incomes of females in each state of the United States, including the District of Columbia and

Puerto Rico, are given in table #2 (“Median income of,” 2013). Create a frequency distribution, relative

frequency distribution, and cumulative frequency distribution using 7 classes. Create a histogram and

relative frequency histogram for the data in table #2. Describe the shape and any findings you can from

the graph.

Table #2: Data of Median Income for Females

$31,862

$60,332

$33,269

$29,548

$42,113

$41,412

$40,993

$40,550

$33,823

$32,684

$33,865

$33,459

$31,330

$29,688

$36,048

$35,438

$31,844

$31,067

$32,462

$31,329

$35,890

$30,752

$37,242

$34,599

$33,424

$35,746

$33,184

$34,381

$41,817

$31,238

$48,748

$35,484

$31,274

$35,301

$40,236

$39,150

$46,185

$41,021

$36,027

$32,843

$47,476

$34,023

$36,931

$47,155

$37,089

$38,177

$40,500

$33,745

$40,416

$32,316

$22,117

$40,969

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