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Stat200 : introduction to statistics final examination, fall 2013

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STAT 200 practice exam

 

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)

 

 

__________

 

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

 

__________

 

3.       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?

 

 

                                                                                                                                                                                ____________

 

 

 

Refer to the following information for Questions 12 and 13.

 

There are 1000 students in the senior class at a certain high school. The high school offers two Advanced Placement math / stat classes to seniors only:  AP Calculus and AP Statistics.  The roster of the Calculus class shows 95 people; the roster of the Statistics class shows 86 people.  There are 43 overachieving seniors on both rosters.

 

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)

 

                The proper distribution for calculating the Confidence Interval is:

                                                                                               

                                                                                                                Chi Square,         t distribution,     z distribution

 

                The lower and upper limits for the 95% confidence interval are:

 

 

 

                                                                                                                                ___________                   ___________  

 

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 seves 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   μ= 750

       H1   μ < 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 α= 0.05 level?

 

                                                                                                                                                                                ____________

                Calculate the test statistic.

 

 

                                                                                                                                                                                ____________

 

What is the P-value for this Hypothesis Test?

 

                                                                                                                                                                _____________

 

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

 

                                                                                                                Null Hypothesis                               Alternate Hypothesis

 

 

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   μ   =   530

H1   μ      530

 

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

 

Calculate the Test Statistic.

 

 

 

 

                                                                                                                                                                ____________

 

What is the P-value for this test?

 

 

 

 

                                                                                                                                                                ____________

 

 

 

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

 

 

 

Do not reject the Null Hypothesis

 

Accept the Alternate Hypothesis

 

                                There is insufficient evidence to make a decision

 

 

 

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?

 

 

                                                                                                                                                _____________

What is the Alternate Hypothesis?

 

 

                                                                                                                                                _____________

 

                                                                                                                               

What is the numerical value of z critical?

 

                                                                                                                                                _____________

 

What is the numerical value of the test statistic?

 

 

 

 

                                                                                                                                                _____________

 

What is the P-value for this Hypothesis test?

 

                                                                                                                                                _____________

 

What is your decision based upon this Hypothesis test?

 

                                                                                                                                                _____________

 

 

 

Refer to the following data for Questions 28 and 29.

 

                           

 

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

 

 

 

 

 

What is the Y intercept of the equation?

 

                                                                                                                                                _____________

 

What is the slope of the equation?

 

                                                                                                                                                _____________

 

 

 

                                                                                                                                   Y = ______  + ______x

 

Answer the following questions to receive full credit for this problem.

 

 

∑x =  _______,                                 ∑y =   _______,                                ∑x2 =  _______,                                ∑xy =   _______

 

 

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 Alternate 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?

 

 

                                                                                                                                                __________________

 

 

 

Having completed the Hypothesis test what is the appropriate decision?

 

 

                                                                                                Null Hypothesis                                Alternate Hypothesis                    

 

 

 

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.

 

                Example question:

 

Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. (1 pt)

 

                A woman experienced a tax audit.  The tax department claimed that the woman was audited because she was randomly selected from all taxpayers.

 

                What type of sampling did the tax department use?

 

32.          Problem 32 is the Honor Pledge.  This question must be answered (truthfully) in the positive in order to receive credit for taking the Final Exam.

 

                                                            

 

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