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STAT200 Introduction to Statistics Final Examination

Question # 00005508
Subject: Statistics
Due on: 12/31/2013
Posted On: 12/16/2013 02:49 PM

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Refer to the following frequency distribution for Questions 1, 2, 3, and 4.

The frequency distribution below shows the distribution for checkout time (in minutes) in UMUC MiniMart between 3:00 PM and 4:00 PM on a Friday afternoon.

Checkout Time (in minutes)

Frequency

1.0 – 1.9

5

2.0 - 2.9

3

3.0 – 3.9

7

4.0 – 4.9

3

5.0 – 5.9

2

1. What percentage of the checkout times was less than 4 minutes? (5 pts)

1. Calculate the mean of this frequency distribution. (10 pts)

3

1. In what class interval must the median lie? (You don’t have to find the median) (5 pts)

4. Assume that the smallest observation in this dataset is 1.2 minutes. Suppose this observation were

incorrectly recorded as .2 instead of 1.2 minutes. (5 pts)

Will the mean increase, decrease, or remain the same?

Will the median increase, decrease or remain the same?

Refer to the following information for Questions 5 and 6

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


5. What is the probability that the outcomes of the second roll is greater than 4, given that the first roll is an even number? (10 pts)

6. Are A and B independent? (5 pts)

Refer to the following data to answer questions 7 and 8.

A random sample of Stat 200 weekly study times in hours is as follows:

4, 14, 15, 17, 20

7. Find the standard deviation. (10 pts)

8. Are any of these study times considered unusual in the sense of our textbook? (2.5 pts)

Does this differ with your intuition? (2.5 pts)

Refer to the following situation for Questions 9, 10, and 11.

The five-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

For each question, give your answer as one of the following: (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. (5 pts each)

9. Which quiz has less interquartile range in grade distribution?

10. Which quiz has the greater percentage of students with grades 90 and over?

11. Which quiz has a greater percentage of students with grades less than 60?

12. What is the probability that a randomly selected senior is in at least one of the two classes?

(10 pts)

13. If the student is in the Calculus class, what is the probability the student is also in the Statistics class? (10 pts)

14. A random sample of 225 SAT scores has a mean of 1500. Assume that SAT scores have a population

standard deviation of 300. Construct a 95% confidence interval estimate of the mean SAT scores.

(15 pts)

Refer to the following information for Questions 15, 16, and 17.

A box contains 5 chips. The chips are numbered 1 through 5. Otherwise, the chips are identical. From this box, we draw one chip at random, and record its value. We then put the chip back in the box. We repeat this process two more times, making three draws in all from this box.

15. How many elements are in the sample space of this experiment? (5 pts)

16. What is the probability that the three numbers drawn are all different? (10 pts)

17. What is the probability that the three numbers drawn are all odd numbers? (10 pts)

Questions 18 and 19 involve the random variable x with probability distribution given below.

X

2

3

4

5

6

P(x)

0.1

0.2

0.4

0.1

0.2

18. Determine the expected value of x. (10 pts)

19. Determine the standard deviation of x. (10 pts)

Consider the following situation for Questions 20 and 21.

Mimi just started her tennis class three weeks ago. On Average, she is able to return 15% of her opponent’s serves. If her opponent serves 10 times, please answer the following questions.

20. Find the probability that she returns at most 2 of the 10 serves from her opponent. (10 pts)

21. How many serves is she expected to return? (5 pts)

22. Given a sample size of 64, with sample mean 730 and sample standard deviation 80, we perform

the following hypothesis test. (20 pts)

Ho ? = 750

H1 ? < 750

What is the appropriate distribution for performing this Hypothesis test?

Z distribution, t distribution, Chi Square distribution, Empirical Rule

What is the critical value of the test statistic at ?= 0.05 level?

What is the P-value for this Hypothesis Test?

What is your conclusion (decision) for this hypothesis test at ?= 0.05 level?

Refer to the following information for Questions 23, 24, and 25.

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

23. What is the probability that a randomly selected pecan tree is between 10 and 12 feet tall? (10 pts)

24. Find the 3rd quartile of the pecan tree distribution. (5 pts)

25. If a random sample of 100 pecan trees is selected, what is the standard deviation of the sample mean? (5 pts)

26. Consider the hypothesis test given by

Ho ? = 530

H1 ? ? 530

In a random sample of 81 subjects, the sample mean is found to be 524. Also, the population standard deviation is ?= 27. (20 pts)

Calculate the Test Statistic.

Is there sufficient evidence to justify the rejection of Ho at ?= 0.01 level?

27. A certain researcher thinks that the proportion of women who say that the earth is getting warmer

is greater than the proportion of men. (25 pts)

In a random sample of 250 women, 70% said that the earth is getting warmer.

In a random sample of 220 men, 68.18% said that the earth is getting warmer.

At the .05 significance level, is there sufficient evidence to support the claim that the proportion of

women saying the earth is getting warmer is higher than the proportion of men saying the earth is

getting warmer?

What is the Null Hypothesis?

28. Find an equation of the least squares regression line. (15 pts)

Complete the following table:

x

y

x^2

xy

y^2

0

4

0

0

16

-1

-2

1

2

4

1

5

1

5

25

2

6

4

12

36

3

8

9

24

64

5

21

15

43

145

What is the Y intercept of the equation?

29 Using the equation you calculated in question 28 What is the predicted value of y if x=4? (10 pts)

30. The UMUC Daily News reported that the color distribution for plain M&M’s was: 40% brown, 20% yellow, 20% orange, 10% green, and 10% 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. (25 pts)

Color

Brown

Yellow

Orange

Green

Tan

Number

45

13

17

7

18

What is the Null Hypothesis?

What is the degrees of freedom for this Hypothesis test?

What is the numerical Chi Square critical value?

What is the numerical value of the Chi Square test statistic?

31. Please note: Each time you re-due the Final Exam the answer to question 31 may change, but the subject matter and format will not change.

Tags examination final statistics introduction stat200 sample test distribution following mean questions value hypothesis deviation probability random standard refer times earth level greater quiz isthe given serves warmer getting color proportion information minutes roll

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Preview: the xxxxx value xxxxxxxx that the xxxxx of the xxxxxx is xxxxxxxxxxxx xxxxx are x * 5 x 5 = xxxxxxxxxxx in xxx xxxxxx space xxxxxxxxxxxxxxx What is xxx probability that xxx three xxxxxxx xxxxx are xxx different? (10 xxxxxx all three xxxxxxx are xxxxxxxxxx xxxx there xxx 5 possible xxxxxxx for the xxxxx value, x xxxxxxxx choices xxx the second xxxxxx and 3 xxxxxxxxxxxxx for xxxxxxxx xxxxx The xxxxx number of xxxxxxxxxxxx with no xxxxxxxx values xx x * x * 3 x 60 With xxx possible xxxxxxxxxxxx xx the xxxxxx space, the xxxxxxxxxxx of drawing xxxxx values xxxx xxx different xxxx each other xxxxxxxxxxxxxxxxxx What is xxx probability xxxx xxx three xxxxxxx drawn are xxx odd numbers? xxx pts)There xxx x odd xxxxxxx available for xxxx draw The xxxxx number xxxxxxxxxxxxxx xxxx have xxx odd values xx 3 * x * x x 27 xxxx 125 possible xxxxxxxxxxxx in the xxxxxx space, xxx xxxxxxxxxxx ofdrawing xxxxx odd values xxxxxxxxxxxxxxxx Questions 18 xxx 19 xxxxxxx xxx random xxxxxxxx x with xxxxxxxxxxx distribution given xxxxx X23456P(x)0 xx xx 40 xx 2 18 xxxxxxxxx the expected xxxxx of x xxx pts)_____________19 xxxxxxxxx the standard xxxxxxxxx of x xxx pts) xxxxxxxxxxxxxxxxxxxxx xxx following xxxxxxxxx for Questions xx and 21 xxxx just xxxxxxx xxx tennis xxxxx three weeks xxx On Average, xxx is xxxx xx return xxx of her xxxxxxxxxxxx serves If xxx opponent xxxxxx xx times, xxxxxx answer the xxxxxxxxx questions 20 xxxx the xxxxxxxxxxx xxxx she xxxxxxx at most x of the xx serves xxxx xxx opponent xxx pts)The probability xxxx she returns xx most x xx the xx serves is xxxxx to the xxx of xxxxxxxxxxxxxxxx xx her xxxxxxxxx 0, 1, xx 2 serves: xxxxx the xxxxxxxx xxxxxxxxxxxxx with x = 10 xxx p = x 15: xxx xxxxx probability xxxxxxxxxxxxxxxxxx How many xxxxxx is she xxxxxxxx to xxxxxxx xx pts)The xxxxxxxx number of xxxxxxxx serves is xxxxx to x x p, xxxxxx is the xxxxxx of serves, xxx p xx xxx probability xxxx Mimi returnsthe xxxxxxxxxxxxxxxxxxxxx Given a xxxxxx size xx xxx with xxxxxx mean 730 xxx sample standard xxxxxxxxx 80, xx xxxxxxx the xxxxxxxxx hypothesis test xxx pts) Ho x = xxx xx ? xxxx 750What is xxx appropriate distribution xxx performing xxxx xxxxxxxxxx test?Z xxxxxxxxxxxxx t distribution, xxx Square distribution, xxxxxxxxx RuleWhat xx xxx critical xxxxx of the xxxx statistic at xx 0 xx xxxxxxxxx critical xxxxx for a xxxxxxxxxxx test with x 0 xx xx -1 xxx ____________Calculate the xxxx statistic The xxxxx of xxx xxxxxxxxxxx is:____________What xx the P-value xxx this Hypothesis xxxxxxxx p-value xx x 0228 xxxxxxxxxxxxxxxxx is your xxxxxxxxxx (decision) for xxxx hypothesis xxxx xx ?= x 05 level? xxxxxx the null xxxxxxxxxx Null xxxxxxxxxx xxxxxxxxx HypothesisRefer xx the following xxxxxxxxxxx for Questions xxx 24, xxx xx The xxxxxxx of pecan xxxxx are normally xxxxxxxxxxx with x xxxx of xx feet and x standard deviation xx 2 xxxx xx What xx the probability xxxx a randomly xxxxxxxx pecan xxxx xx between xx and 12 xxxx tall? (10 xxxx _____________24 .....
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