# ‘EXTREME ACCURACY & ATTENTION TO DETAILS’/ EACH QUESTION MUST BE ANSWERED ON THE ANSWER SHEET AND PLEASE SHOW WORK WHEN APPLICABLE

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Quiz

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Question 1 (24 points)

Question 1:

True or False.

Enter the answer to each of the the questions with:

T for True

F for False

(a)      If all the observations in a data set are identical, then the variance for this data set is zero.

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

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

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

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(e) In a two-tailed hypothesis testing at significance level α of 0.05, the test statistic is calculated as 2. If P(X >2) = 0.03, then we have sufficient evidence to reject the null hypothesis.

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Question 2 (5 points)

Question 2 options:

Refer to the following frequency distribution for Questions 2, 3, 4, and 5.

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

A random sample of 100 students was chosen from UMUC STAT 200 classes. The frequency distribution below shows the distribution for study time each week (in hours).

 Checkout Time (in minutes) Frequency Relative Frequency 0.0 – 4.9 5 A 5.0 – 9.9 13 B 10.0 – 14.9 C 22 15.0 – 19.9 42 D 20.0 – 24.9 E F Total 100 G

Complete the Frequency Table with the missing frequency and relative frequency numbers.

Enter answer for “A” as a decimal with 2 decimal places with a zero to the left of the decimal point.

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Enter answer for “B” as a decimal with 2 decimal places with a zero to the left of the decimal point.

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Enter answer for “C” as an Integer.

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Enter answer for “D” as a decimal with 2 decimal places with a zero to the left of the decimal point.

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Enter answer for “E” as an integer.

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Enter answer for “F” as a decimal with 2 decimal places with a zero to the left of the decimal point.

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Question 3 (5 points)

Question 3 options:

A random sample of 100 students was chosen from UMUC STAT 200 classes. The frequency distribution below shows the distribution for study time each week (in hours).

This is the same distribution table from Question 2

 Checkout Time (in minutes) Frequency Relative Frequency 0.0 – 4.9 5 A 5.0 – 9.9 13 B 10.0 – 14.9 C 22 15.0 – 19.9 42 D 20.0 – 24.9 E F Total 100 G

What percentage of the study times was at least 15 hours?

Enter answer as a percent without the percent sign to 0 decimal places.

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Question 4 (5 points)

Question 4 options:

A random sample of 100 students was chosen from UMUC STAT 200 classes. The frequency distribution below shows the distribution for study time each week (in hours).

This is the same distribution table from Question 2

 Checkout Time (in minutes) Frequency Relative Frequency 0.0 – 4.9 5 A 5.0 – 9.9 13 B 10.0 – 14.9 C 22 15.0 – 19.9 42 D 20.0 – 24.9 E F Total 100 G

Enter answer by selecting the appropriate letter.

a     Interval 1    (0.0 – 4.9)

b     Interval 2    (5.0 – 9.9)

c     Interval 3    (10.0 – 14.9)

d     Interval 4    (15.0 – 19.9)

e     Interval 5    (20.0 – 24.9)

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Question 5 (5 points)

Question 5 options:

A random sample of 100 students was chosen from UMUC STAT 200 classes. The frequency distribution below shows the distribution for study time each week (in hours).

This is the same distribution table from Question 2.

 Checkout Time (in minutes) Frequency Relative Frequency 0.0 – 4.9 5 A 5.0 – 9.9 13 B 10.0 – 14.9 C 22 15.0 – 19.9 42 D 20.0 – 24.9 E F Total 100 G

The distribution is negatively skewed, symetrical, positively skewed?

Answer question by entering appropriate letter.

a     negatively skewed

b     symetrical

c     positively skewed

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Question 6 (5 points)

Question 6 options:

A fair 6-faced die is rolled two times. Let A be the event that the outcome of the first roll is a multiple of 3, and B be the event that the outcome of second roll is greater than 4.

How many outcomes are there in the sample space?

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Question 7 (10 points)

Question 7 options:

A 6-faced die is rolled two times.  Let A be the event that the outcome of the first roll is an even number, and B be the event that the outcome of the second roll is greater than 4.

What is the probability that the outcome of the second roll is greater than 4, given that the first roll is an even number?

Enter answer as a reduced fraction or a decimal rounded to 2 decimal places.

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Question 8 (5 points)

Question 8 options:

A fair 6-faced die is rolled two times. Let A be the event that the outcome of the first roll is a multiple of 3, and B be the event that the outcome of second roll is greater than 4.

Are A and B independent?

Enter answer by selecting the appropriate letter.

a    Yes  The events are independant

b    No    The events are dependant

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Question 9 (5 points)

Question 9 options:

The 5 number summary below shows the grade distribution of two Stat 200 quizzes.

 Minimum Q1 Median Q3 Maximum Quiz 1 12 40 60 95 100 Quiz 2 20 35 50 90 100

Which quiz has less interquartile range in grade distribution?

a   Quiz 1

b   Quiz 2

c   Both quizzes have the same value requested.

d   It is impossible to tell using only the given information.

Answer the question by keying in the appropriate letter.

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Question 10 (5 points)

Question 10 options:

The 5 number summary below shows the grade distribution of two Stat 200 quizzes.

 Minimum Q1 Median Q3 Maximum Quiz 1 12 40 60 95 100 Quiz 2 20 35 50 90 100

Which quiz has the greater percentage of students with grades of 90 or over?

a   Quiz 1

b   Quiz 2

c   Both quizzes have the same value requested.

d   It is impossible to tell using only the given information.

Answer the question by keying in the appropriate letter.

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Question 11 (5 points)

Question 11 options:

The 5 number summary below shows the grade distribution of two Stat 200 quizzes.

 Minimum Q1 Median Q3 Maximum Quiz 1 12 40 60 95 100 Quiz 2 20 35 50 90 100

Which quiz has lthe greatest number of students with grades less than 60?

a   Quiz 1

b   Quiz 2

c   Both quizzes have the same value requested.

d   It is impossible to tell using only the given information.

Answer the question by keying in the appropriate letter.

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Question 12 (10 points)

Question 12 options:

There are 1000 juniors in a college.

Among the 1000 juniors

300 students are taking STAT200

150 students are taking PSYC300

There are 50 students taking both courses.

What is the probability that a randomly selected junior is taking at least one of these two courses?
Enter answer as a 2 place decimal or a reduced fraction.

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Question 13 (10 points)

Question 13 options:

There are 1000 juniors in a college.

Among the 1000 juniors

300 students are taking STAT200

150 students are taking PSYC300

There are 50 students taking both courses.

What is the probability that a randomly selected junior is taking PSYC300, given that she is taking STAT200?

Enter answer as a 2 place decimal with a zero to the left of the decimal point or a reduced fraction.

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Question 14 (5 points)

Question 14 options:

There are 8 books in the “Statistic is Fun” series.  Mimi would like to choose 2 books from the series for her summer reading.

How many different ways can the two books be selected?

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Question 15 (15 points)

Question 15 options:

Let random variable x represent the number of girls in a family of three children.

Construct a table describing the probability distribution.

(You can assume the probability of having a female child is .5 and the gender of each children is independant of each of the others.)

 x P(x) 0 A 1 B 2 C 3 D

Enter the probability of “A” as a reduced fraction or a 3 place decimal.

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Enter the probability of “B” as a reduced fraction or a 3 place decimal.

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Enter the probability of “C” as a reduced fraction or a 3 place decimal.

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Enter the probability of “D” as a reduced fraction or a  3 place decimal.

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Determine the mean and standard deviation of x.
Enter the mean as a 1 place decimal and the standard deviation rounded to 2 decimal places in the order asked for.

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Question 16 (20 points)

Question 16 options:

Rabbits like to eat the cucumbers in Mimi’s garden. There are 10 cucumbers in hergarden which will be ready to harvest in about 10 days.
Based on her experience, the probabilityof a cucumber being eaten by the rabbits before harvest is 0.60.

Let X be the number of cucumbers that Mimi harvests (that is, the number of cucumbers not eatenby rabbits).  As we know, the distribution of X is a binomial probability distribution.

What is thenumber of trials (n), probability of successes (p) and probability of failures (q), respectively?
Enter number of trials as an integer and probabilities as a 1 decimal with1 place precision with a 0 to the left of the decimal point.

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Find the probability that Mimi harvests at least 2 of the 10 cucumbers.

Enter answer rounded to 3 decimal places.
Do not enter answer as a percent.

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How many cucumbers can she expect to harvest?
Enter answer with 0 decimal places. (integer)

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Question 17 (10 points)

Question 17 options:

The heights of pecan trees are normaily distributed with a mean of 10 feet and a standard deviation of 2 feet.

What is the probability that a randomly selected pecan tree is between 9 and 12 feet tall.

Enter answer as a decimal rounded to 4 decimal places with a 0 to the left of the decimal point.
Do not enter answer as a percent.

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Question 18 (5 points)

Question 18 options:

The heights of pecan trees are normaily distributed with a mean of 10 feet and a standard deviation of 2 feet.

Find the 80th percentile of the pecan tree height distribution.
Enter answer as a decimal rounded to 1 decimal place.

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Question 19 (5 points)

Question 19 options:

The heights of pecan trees are normaily distributed with a mean of 10 feet and a standard deviation of 2 feet.

If a random sample of of 225 pecan trees is selected, what is the standard deviation of the sample mean,
Enter answer as a 2 place decimal or a reduced fraction,

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Question 20 (10 points)

Question 20 options:

Arandom sample of 100 SAT scores has a sample mean of 1500 hours.

Assume that the statistic scores have a population standard deviation of 300 hours.

Construct a 95% confidence interval estimate of the mean SAT scores.

Enter the lower and upper confidence limit numbers rounded to 1 decimal place.
Enter the lower confidence interval number first and then the upper confidence interval number.

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Question 21 (15 points)

Question 21 options:

Consider the hypothesis test given by

Ho: p = 0.5

H1: p < 0.5

In a random sample of 100  subjects, the sample proportion is found to be phat = 0.47

What is the appropriate distribution for performing the hypothesis test?

a    Uniform distribution

b     z distribution

c     t distribution

d     Chi square distribution

e     F distribution

Enter appropriate letter for answering this question.

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Determine the numerical value of the test statistic.

Enter answer rounded to 1 decimal place with a zero to the left of the decimal point.

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Determine the p-value for this test.

Enter answer rounded to 3 decimal places with a zero to the left of the decimal point.

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Is there sufficient evidence to justify the rejection of Ho at an α = .01 level?

a     Yes: There is sufficient evidence to justify the rejection of Ho at an α = .01 level

b     No:  There is insufficient evidence to justify the rejection of Ho at an α = .01 level

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Question 22 (20 points)

Question 22 options:

Mimi was curious if regular excise really helps weight loss, hence she decided to perform a hypothesis test.
A random sample of 5 UMUC students was chosen. The students took a 30-minute exercise every day for 6 months.
Ther weight for each individual was recorded before and after the exercise regimen.

Does the data below suggest that the regular exercise helps weight loss using a 0.01 significance level to test the claim.?

 Weight in Pounds Subjects Before After 1 159 130 2 170 160 3 185 180 4 165 165 5 200 190

Identify the null hypothesis and the alternative hypothesis.

a     Ho     There is no weight loss due to exercising everyday.
Ha     Regular daily exercise effects weight loss.

b     Ho     Regular daily exercise helps weight loss.
Ha     There is no weight loss due to exercising everyday.

c     Ho     There is no weight loss due to exercising everyday.
Ha     Regular daily exercise helps weight loss.

Enter the correct answer by selecting the appropriate letter.

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The appropriate distribution for performing the hypothesis test is:

a     Uniform distribution.

b     z distribution

c     t distribution

d     Chi Square distribution

What is number of degrees of freedom (dF)?

Enter the appropriate letter for selecting the correct distribution followed by the dF.
Enter 0 for the dF if this is an inappropriate question for the distribution selected.

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What is the numerical value of the test statistic?
Enter answer rounded to 2 decimal places.

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What is the numerical value of the Pvalue.
Enter answer rounded to 2 decimal places with a zero to the left of the decimal point.

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Is there sufficient evidence to support the alternate hypothesis?

a     There is insufficient evidence to support the alternate hypothesis.

b     There is sufficient evidence to support the alternate hypothesis.

c    There is insufficient evidence to draw any conclusion from the hypothesis test.

Enter the answer to this question by selecting the appropriate letter.

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Question 23 (10 points)

Question 23 options:

A Stat 200 instructor is interested in whether there is any variation in the final grades between her two classes.

Data collected from the two classes are as follows:

Section 1         n1 = 31             x1 = 78             s1 = 10

Section 2         n2 = 30             x2 = 72             s2 = 14

The instructor’s null hypothesis and alternative hypothesis are:

H0:        σ1 = σ2           and      Ha:        σ1 < σ2

The appropriate distribution for performing the hypothesis test is:

a     Uniform distribution.

b     z distribution

c     t distribution

d     Chi Square distribution

e     F distribution

Enter the appropriate letter for selecting the correct distribution.

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Determine the test statistic for the hypotesis test.
Enter test statistic rounded to 2 decimal places with a zero to the left of the decimal point.

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Determine the p-value for this test.
Enter P value rounded to 2 decimal places with a zero to the left of the decimal point.

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Is there sufficient evidence to justify the rejection of the H0 at the α = .05 level.

a     Yes     There is sufficient evidence to justify the rejection of the H0 at the α = .05 level.
b     No      There is insufficient evidence to justify the rejection of the H0 at the α = .05 level.

Enter the letter that is appropriate answer for this question.

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Question 24 (20 points)

Question 24 options:

A random sample of 4 professional athletes produced the following data where x is the number of endorsements a player
has and y is the amount of money made (in millions of dollars).

 x 0 1 3 5 y 1 2 3 8

Find the equation of the least squares regression line.
Round each answer to 2 decimal place with the “constant” followed by the “slope”.

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Based on the above equation, what is the predicted value of y if x = 4?
Round answer to 1 decimal place.

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Question 25 (15 points)

Question 25 options:

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

40% brown

20% yellow

20% orange

10% green

10% tan

Each piece of candy in a random sample of 100 plain M&m’s was clasified 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.

 Color Brown Yellow Orange Green tan Number 42 21 12 7 18

Identify the null hypothesis by selecting the appropriate letter a or b.

a    The color distribution for plain M&M ‘s is not in agreement with what was reported in the UMUC Daily News.

b    The color distribution for plain M&M ‘s is in agreement with what was reported in the UMUC Daily News.

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Identify the alternative hypothesis by selecting the appropriate letter c or d.

c    The color distribution for plain M&M ‘s is not in agreement with what was reported in the UMUC Daily News.

d    The color distribution for plain M&M ‘s is in agreement with what was reported in the UMUC Daily News.

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The appropriate distribution for performing the hypothesis test is:

a     Uniform distribution.

b     z distribution

c     t distribution

d     Chi Square distribution

e     F Distribution

What is number of degrees of freedom (dF)?

Enter the appropriate letter for selecting the correct distribution followed by the dF.
Enter 0 for the dF if this is an inappropriate question for the distribution selected.

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What is the numerical value of the test statistic?
Round answer to 1 decimal place.

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What is the numerical value of the Pvalue?
Round answer to 2 decimal place.

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Is there sufficient evidence to support the claim that the published color distribution is correct??

Enter the appropriate letter for the correct answer.

a     The Ho hypothesis is rejected.  The Pvalue is less than the significance level,

b    The Ho hypothesis is not rejected.  The Pvalue is greater than than the significance level.

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Problem Number

Solution

1

(25 pts)

(a)

(b)

(c)

(d)

(e)

Work for (a), (b), (c), (d) and (e):

2

(5 pts)

 Study Time (in hours) Frequency Relative Frequency 0.0 – 4.9 5 5.0 – 9.9 13 10.0 – 14.9 0.22 15.0 -19.9 42 20.0 – 24.9 Total 100

Work:

3

(5 pts)

Work:

4

(5 pts)

Work:

5

(5 pts)

Work:

6

(5 pts)

Work:

7

(10 pts)

Work:

8

(5 pts)

Work:

9

(5 pts)

Work:

10

(5 pts)

Work:

11

(5 pts)

Work:

12

(10 pts)

Work:

13

(10 pts)

Work:

14

(5 pts)

Work:

15

(15 pts)

(a)

 x P(x) 0 1 2 3

(b) mean = __________ , and standard deviation =  _____________

Work for (a) and (b):

16

(20 pts)

(a)

(b)

(c)

Work for (a), (b) and (c) :

17

(10 pts)

Work:

18

(5 pts)

Work:

19

(5 pts)

Work:

20

(10 pts)

Work:

21

(15 pts)

(a)

(b)

(c)

Work for (a), (b) and (c):

22

(20 pts)

(a)

(b)

(c)

(d)

Work for (b) and (c):

23

(10 pts)

(a)

(b)

(c)

Work for (a), (b) and (c):

24

(20 pts)

(a)

(b)

Work for (a) and (b):

25

(15 pts)

(a)

(b)

(c)

(d)

Work for (b) and (c):

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