# stat200 Final Examination, Summer 2016 OL1 A+

If P(A) = 0.4, P(B) = 0.5, and A and B are independent, then P(A AND B) = 0.9.

If the variance of a data set is 0, then all the observations in this data set must be zero.

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

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

In a two-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 0.03,

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)

Among the Senators in the current Congress, 54% are Republicans. 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)

In a career readiness research, 100 students were randomly selected from the psychology

program, 150 students were randomly selected from the communications program, and 120

students were randomly selected from cyber security program. This type of sampling is called:

(i)

(ii)

(iii)

(iv)

cluster

convenience

systematic

stratified

STAT 200: Introduction to Statistics

Final Examination, Summer 2016 OL1

Page 3 of 7

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

Frequency Relative Frequency

50 - 69

24

70 - 89

228

90 -109

493

0.23

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 OL1

Page 4 of 7

The five-number summary below shows the grade distribution of two STAT 200 quizzes for a

sample of 500 students.

Quiz 1

Quiz 2

Minimum

Q1

Median

Q3

Maximum

15

20

35

35

55

50

85

90

100

100

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 less range in grade distribution?

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

Which quiz has a 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 with replacement.

Assuming the two random selections are made without replacement.

7.

There are 1000 students in a high school. Among the 1000 students, 250 students take AP

Statistics, and 300 students take AP French. 100 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 complement event of (S OR F).

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

8.

Consider rolling two fair dice. Let A be the event that the sum of the two dice is 8, and B be

the event that the first one is a multiple of 3.

(a)

What is the probability that the sum of the two dice is 8 given that the first one is a multiple of

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

Are event A and event B independent? Explain.

(b)

STAT 200: Introduction to Statistics

Final Examination, Summer 2016 OL1

Page 5 of 7

9.

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

work, will receive no credit).

(a)

UMUC Stat Club is sending a delegate of 2 members to attend the 2016 Joint Statistical

Meeting in Chicago. There are 10 qualified candidates. How many different ways can the

delegate be selected?

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)

-2

0.1

0

0.1

1

0.3

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 least 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?

13.

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

(a)

(b)

If the variance of a data set is 0, then all the observations in this data set must be zero.

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

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

In a two-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 0.03,

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)

Among the Senators in the current Congress, 54% are Republicans. 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)

In a career readiness research, 100 students were randomly selected from the psychology

program, 150 students were randomly selected from the communications program, and 120

students were randomly selected from cyber security program. This type of sampling is called:

(i)

(ii)

(iii)

(iv)

cluster

convenience

systematic

stratified

STAT 200: Introduction to Statistics

Final Examination, Summer 2016 OL1

Page 3 of 7

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

Frequency Relative Frequency

50 - 69

24

70 - 89

228

90 -109

493

0.23

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 OL1

Page 4 of 7

The five-number summary below shows the grade distribution of two STAT 200 quizzes for a

sample of 500 students.

Quiz 1

Quiz 2

Minimum

Q1

Median

Q3

Maximum

15

20

35

35

55

50

85

90

100

100

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 less range in grade distribution?

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

Which quiz has a 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 with replacement.

Assuming the two random selections are made without replacement.

7.

There are 1000 students in a high school. Among the 1000 students, 250 students take AP

Statistics, and 300 students take AP French. 100 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 complement event of (S OR F).

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

8.

Consider rolling two fair dice. Let A be the event that the sum of the two dice is 8, and B be

the event that the first one is a multiple of 3.

(a)

What is the probability that the sum of the two dice is 8 given that the first one is a multiple of

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

Are event A and event B independent? Explain.

(b)

STAT 200: Introduction to Statistics

Final Examination, Summer 2016 OL1

Page 5 of 7

9.

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

work, will receive no credit).

(a)

UMUC Stat Club is sending a delegate of 2 members to attend the 2016 Joint Statistical

Meeting in Chicago. There are 10 qualified candidates. How many different ways can the

delegate be selected?

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)

-2

0.1

0

0.1

1

0.3

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 least 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?

13.

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

(a)

(b)

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