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(Solved) STAT 200: Introduction to Statistics Final Examination, Summer


Ram_81 Can you please complete the attached file and return it to me by Sunday at 10pm. I already completed it on my own but would like to check my answers before I submit it. Please use the attached answer sheet and please answer all the questions thoroughly and justify your choices for the multiple choice questions and show all work for all other questions. As previously I will leave a big tip when it's completed. Thank you for your help.


STAT 200: Introduction to Statistics

 


 

Final Examination, Summer 2016 OL3/US2

 


 

Page 1 of 8

 


 

STAT 200

 

OL3/US2 Sections

 

Final Exam

 

Summer 2016

 

The final exam will be posted at 12:01 am on August 5, and it is

 

due at 11:59 pm on August 7, 2016. Eastern Time is our reference

 

time.

 


 

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 UMUC Academic Dishonesty and Plagiarism policy to use

 

unauthorized materials or work from others.

 

Answer all 20 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 200 total points; 10 points for each question.

 

You must include the Honor Pledge on the title page of your submitted final exam.

 

Exams submitted without the Honor Pledge will not be accepted.

 


 

STAT 200: Introduction to Statistics

 


 

1.

 


 

Final Examination, Summer 2016 OL3/US2

 


 

Page 2 of 8

 


 

True or False. Justify for full credit.

 

(a)

 

(b)

 

(c)

 

(d)

 

(e)

 


 

If P(A) = 0.4, P(B) = 0.5, and A and B are independent, then P(A AND B) = 0.2.

 

If all the observations in a data set are identical, then the variance of this data set is 0.

 

The mean is always equal to the median for a normal distribution.

 

A 90% confidence interval is wider than a 95% confidence interval of the same parameter.

 

In a right-tailed test, the value of the test statistic is 2. The test statistic follows a distribution

 

with the distribution curve shown below. If we know the shaded area is 0.96, then we have

 

sufficient evidence to reject the null hypothesis at 0.05 level of significance.

 


 

2.

 


 

Choose the best answer. Justify for full credit.

 


 

(a)

 


 

UMUC Stat Club conducted a survey on STAT 200 study hours. The survey result showed

 

that 54% of the respondents spent more than 20 hours each week on STAT 200. The value

 

54% 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)

 


 

UMUC STAT Club wanted to estimate the study hours of STAT 200 students. Two STAT 200

 

sections were randomly selected and all students from these two sections were asked to fill out

 

the questionnaire. This type of sampling is called:

 

(i)

 

(ii)

 

(iii)

 

(iv)

 


 

cluster

 

convenience

 

systematic

 

stratified

 


 

STAT 200: Introduction to Statistics

 


 

Final Examination, Summer 2016 OL3/US2

 


 

Page 3 of 8

 


 

3.

 


 

Choose the best answer. Justify for full credit.

 


 

(a)

 


 

A study of 10 different weight loss programs involved 500 subjects. Each of the 10 programs

 

had 50 subjects in it. The subjects were followed for 12 months. Weight change for each

 

subject was recorded. You want to test the claim that the mean weight loss is the same for the

 

10 programs. What statistical approach should be used?

 

(i)

 

t-test

 

(ii)

 

linear regression

 

(iii)

 

ANOVA

 

(iv)

 

confidence interval

 


 

(b)

 


 

A STAT 200 instructor teaches two classes. She wants to test if the variances of the score

 

distribution for the two classes are different. What type of hypothesis test should she use?

 

(i)

 

t-test for two independent samples

 

(ii)

 

t-test for matched samples

 

(iii)

 

z-test for two samples

 

(iv)

 

F- test

 


 

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

 

50 - 69

 


 

Frequency Relative Frequency

 

24

 

0.25

 


 

70 - 89

 

90 -109

 


 

455

 


 

110 - 129

 


 

(a)

 

(b)

 

(c)

 


 

130 - 149

 


 

25

 


 

Total

 


 

1000

 


 

Complete the frequency table with frequency and relative frequency. Express the relative

 

frequency to three decimal places.

 

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

 

Does this distribution have positive skew or negative skew? Why or why not?

 


 

STAT 200: Introduction to Statistics

 


 

5.

 


 

Final Examination, Summer 2016 OL3/US2

 


 

Page 4 of 8

 


 

The boxplots below show the grade distribution of two STAT 200 quizzes for a sample of 500

 

students.

 


 

For each question, give your answer as one of the following: (i) Quiz 1; (ii) Quiz 2; (iii) Both quizzes

 

have the same value requested; (iv) It is impossible to tell using only the given information. Then

 

explain your answer in each case.

 

(a)

 

(b)

 

(c)

 


 

Which quiz has the greater range in grade distribution?

 

Which quiz has the lower percentage of students with grades 85 and over?

 

Which quiz has the greater percentage of students with grades less than 60?

 


 

6.

 


 

A sample of 10 LED light bulbs consists of 1 defective and 9 good light bulbs. A quality

 

control technician wants to randomly select two of the light bulbs for inspection. Find the

 

probability that the first selected light bulb is good and the second light bulb is also good.

 

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

 


 

(a)

 

(b)

 


 

Assuming the two random selections are made without replacement.

 

Assuming the two random selections are made with replacement.

 


 

7.

 


 

There are 1000 students in a high school. Among the 1000 students, 200 students take AP

 

Statistics, and 250 students take AP French. 50 students take both AP courses. Let S be the

 

event that a randomly selected student takes AP Statistics, and F be the event that a randomly

 

selected student takes AP French. Show all work. Just the answer, without supporting work,

 

will receive no credit.

 


 

(a)

 

(b)

 


 

Provide a written description of the event (S OR F).

 

What is the probability of the complement event of (S OR F)?

 


 

STAT 200: Introduction to Statistics

 


 

Final Examination, Summer 2016 OL3/US2

 


 

Page 5 of 8

 


 

8.

 


 

Consider rolling two fair dice. Let A be the event that the sum of the two dice is 7, and B be

 

the event that the first one is an even number.

 


 

(a)

 


 

What is the probability that the sum of the two dice is 7 given that the first one is an even

 

number? Show all work. Just the answer, without supporting work, will receive no credit.

 

Are event A and event B independent? Explain.

 


 

(b)

 


 

9.

 


 

Answer the following two questions. (Show all work. Just the answer, without supporting

 

work, will receive no credit).

 


 

(a)

 


 

There are 15 juniors and 20 seniors in the UMUC Stat Club. The club is to send four

 

representatives to the Joint Statistical Meetings. If the members of the club decide to send two

 

juniors and two seniors, how many different groupings are possible?

 

A bike courier needs to make deliveries at 6 different locations. How many different routes can

 

he take?

 


 

(b)

 


 

10.

 


 

Assume random variable x follows a probability distribution shown in the table below.

 

Determine the mean and standard deviation of x. Show all work. Just the answer, without

 

supporting work, will receive no credit.

 

x

 

P(x)

 


 

-1

 

0.3

 


 

0

 

0.1

 


 

1

 

0.1

 


 

2

 

0.2

 


 

3

 

0.3

 


 

11.

 


 

Rabbits like to eat the cucumbers in Mimi?s garden. There are 10 cucumbers in her garden

 

which will be ready to harvest in about 10 days. Based on her experience, the probability of a

 

cucumber being eaten by the rabbits before harvest is 0.30.

 


 

(a)

 


 

Let X be the number of cucumbers that Mimi harvests (that is, the number of cucumbers not

 

eaten by rabbits). As we know, the distribution of X is a binomial probability distribution.

 

What is the number of trials (n), probability of successes (p) and probability of failures (q),

 

respectively?

 

Find the probability that Mimi harvests at most 8 of the 10 cucumbers. (round the answer to 3

 

decimal places) Show all work. Just the answer, without supporting work, will receive no credit.

 


 

(b)

 


 

12.

 


 

Assume the weights of men are normally distributed with a mean of 170 lbs and a standard

 

deviation of 30 lbs. Show all work. Just the answer, without supporting work, will receive no

 

credit.

 


 

(a)

 

(b)

 


 

Find the 75th percentile for the distribution of men?s weights.

 

What is the probability that a randomly selected man weighs more than 200 lbs?

 


 

STAT 200: Introduction to Statistics

 


 

13.

 


 

(a)

 

(b)

 


 

Final Examination, Summer 2016 OL3/US2

 


 

Page 6 of 8

 


 

Assume the SAT Mathematics Level 2 test scores are normally distributed with a mean of 500

 

and a standard deviation of 100. Show all work. Just the answer, without supporting work, will

 

receive no credit.

 

If a random sample of 64 test scores is selected, what is the standard deviation of the sample

 

mean?

 

What is the probability that 64 randomly selected test scores will have a mean test score that is

 

between 475 and 525?

 


 

14.

 


 

A survey showed that 80% of the 1600 adult respondents believe in global warming. Construct a

 

90% confidence interval estimate of the proportion of adults believing in global warming. Show

 

all work. Just the answer, without supporting work, will receive no credit.

 


 

15.

 


 

In a study designed to test the effectiveness of garlic for lowering cholesterol, 49 adults were

 

treated with garlic tablets. Cholesterol levels were measured before and after the treatment. The

 

changes in their LDL cholesterol (in mg/dL) have a mean of 3 and standard deviation of 14.

 

Construct a 95% confidence interval estimate of the mean change in LDL cholesterol after the

 

garlic tablet treatment. Show all work. Just the answer, without supporting work, will receive

 

no credit.

 


 

16.

 


 

Mimi is interested in testing the claim that banana is the favorite fruit for more than 50% of the

 

adults. She conducted a survey on a random sample of 100 adults. 58 adults in the sample

 

chose banana as their favorite fruit.

 

Assume Mimi wants to use a 0.10 significance level to test the claim.

 


 

(a)

 

(b)

 

(c)

 

(d)

 


 

17.

 


 

Identify the null hypothesis and the alternative hypothesis.

 

Determine the test statistic. Show all work; writing the correct test statistic, without supporting

 

work, will receive no credit.

 

Determine the P-value for this test. Show all work; writing the correct P-value, without

 

supporting work, will receive no credit.

 

Is there sufficient evidence to support the claim that banana is the favorite fruit for more than

 

50% of the adults? Explain.

 

In a study of freshman weight gain, the measured weights of 5 randomly selected college

 

students in September and April of their freshman year are shown in the following table.

 


 

Student

 

1

 

2

 

3

 

4

 

5

 


 

Weight (kg)

 

September

 

April

 

67

 

66

 

53

 

55

 

64

 

68

 

71

 

70

 

70

 

75

 


 

Is there evidence to suggest that the mean weight of the freshmen in April is greater than the

 

mean weight in September?

 


 

STAT 200: Introduction to Statistics

 


 

Final Examination, Summer 2016 OL3/US2

 


 

Page 7 of 8

 


 

Assume we want to use a 0.10 significance level to test the claim.

 

(a)

 

(b)

 

(c)

 

(d)

 


 

18.

 


 

(a)

 

(b)

 

(c)

 

(d)

 


 

19.

 


 

Identify the null hypothesis and the alternative hypothesis.

 

Determine the test statistic. Show all work; writing the correct test statistic, without supporting

 

work, will receive no credit.

 

Determine the P-value for this test. Show all work; writing the correct P-value, without

 

supporting work, will receive no credit.

 

Is there sufficient evidence to support the claim that the mean weight of the freshmen in April

 

is greater than the mean weight in September? Justify your conclusion.

 

In a pulse rate research, a simple random sample of 81 men results in a mean of 75 beats per

 

minute, and a standard deviation of 12 beats per minute. Based on the sample results, the

 

researcher concludes that the pulse rates of men have a standard deviation greater than 10 beats

 

per minutes. Use a 0.05 significance level to test the researcher?s claim.

 

Identify the null hypothesis and alternative hypothesis.

 

Determine the test statistic. Show all work; writing the correct test statistic, without

 

supporting work, will receive no credit.

 

Determine the P-value for this test. Show all work; writing the correct P-value, without

 

supporting work, will receive no credit.

 

Is there sufficient evidence to support the researcher?s claim? Explain.

 


 

The UMUC Daily News reported that the color distribution for plain M&M?s was: 30%

 

brown, 30% yellow, 10% orange, 10% green, and 20% tan. Each piece of candy in a random

 

sample of 100 plain M&M?s was classified according to color, and the results are listed below.

 

Use a 0.05 significance level to test the claim that the published color distribution is correct.

 

Show all work and justify your answer.

 

Color

 

Number

 


 

Brown

 

37

 


 

Yellow

 

26

 


 

Orange

 

12

 


 

Green

 

7

 


 

Tan

 

18

 


 

(a) Identify the null hypothesis and the alternative hypothesis.

 

(b) Determine the test statistic. Show all work; writing the correct test statistic, without

 

supporting work, will receive no credit.

 

(c) Determine the P-value. Show all work; writing the correct P-value, without supporting

 

work, will receive no credit.

 

(d) Is there sufficient evidence to support the claim that the published color distribution is

 

correct? Justify your answer.

 


 

STAT 200: Introduction to Statistics

 


 

20.

 


 

(b)

 


 

Page 8 of 8

 


 

A STAT 200 instructor believes that the average quiz score is a good predictor of final exam

 

score. A random sample of 5 students produced the following data where x is the average quiz

 

score and y is the final exam score.

 

x

 

y

 


 

(a)

 


 

Final Examination, Summer 2016 OL3/US2

 


 

90

 

145

 


 

50

 

150

 


 

60

 

130

 


 

100

 

180

 


 

70

 

120

 


 

Find an equation of the least squares regression line. Show all work; writing the correct

 

equation, without supporting work, will receive no credit.

 

Based on the equation from part (a), what is the predicted final exam score if the average quiz

 

score is 80? Show all work and justify your answer.

 


 

 


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