Project #43162 - Stat Final

 

1.              Determine whether the given value is a statistic or a parameter.            (4 pts)

a)              In a STAT 200 student survey, 20% of the respondents said that they had to take time off from work to study for the course.

                                                                                                                                                Statistic                                   Parameter  

b)              The average lifetime of all street lights in School Academic Center is 20,000 hours.

Statistic                                   Parameter

Refer to the following frequency distribution for Questions 4, 5, 6, and 7.

 

2.              Determine whether the given statement is True or False. (8 pts)

                 

a)     The Mean is a better measure of the center than the Median because the Mean is not affected by extreme values from a data set.

 

True        False

 

 

b)     If the variance from the data set is zero, then all the observations in this data set are the same.

True        False

 

 

c)     Is it possible that a data set does not have a mode?

True        False

 

 

d)     P(A and “not A”) = 1, where “not A” is the complement of A?

 

 

True        False


 

Refer to the following frequency distribution for Questions 3, 4, 5, and 6.  Show all work.  Just the answer, without supporting work, will receive no credit,

 

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

 

Checkout Time (in minutes)

Frequency

1.0 – 1.9

6

2.0 - 2.9

5

3.0 – 3.9

4

4.0 – 4.9

3

5.0 – 5.9

2

 

 

3.     What percentage of the checkout times was at least 4 minutes? (5 pts)

 

__________

 

4.     Calculate the mean of this frequency distribution. (5 pts)

 

 

 

 

__________

 

5.     Calculate the standard deviation of this frequency distribution. (10 pts)

 

 

 

 

__________

 

6.    Assume that the smallest observation in this dataset is 1.2 minutes.  Suppose this observation was

        incorrectly recorded as .12 instead of 1.2 minutes. (5 pts)

 

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

 

Increase                Decrease             Remain the same

 

        Will the Median increase, decrease or remain the same?

 

Increase                Decrease             Remain the same

Refer to the following information for Questions 7 and 8

 

A random sample of Stat200 weekly study times in hours is as follows:

 

1      13     15     18     20

 

7.       Find the standard deviation. (Round answer to two decimal places.) (10 pts)

 

 

 

____________

 

8.       Are any of these times considered unusual based on the Range Rule of Thumb? (5 pts)

Explain your approach and show work.

 

      Yes           No

Refer to the following information for Questions 9, 10 and 11.  Show all work.  Just the answers without supporting work will receive no credit.

 

Consider selecting one card at a time without replacement from a 52-card deck.  Let event A be the first card is a heart, and event B be the second card is a heart.

 

 

9.       What is the probability that the first card is a heart and the second card is also a heart? (8 pts)

Express answer as a fraction.

 

                                                                                                                                                                                                      ____________

 

 

10.       What is the probability that the second card is a heart, given that the first card is a heart? (8pts)

Express answer as a fraction.

 

____________

 

11.       Are A and B independent? (2pts)

Explain your answer

        Yes         No

 

 

 

 

 

Refer to the following data to answer questions 12 and 13.

 

There are 1500 juniors in a college.  Among the 1500 juniors, 200 students are taking Stat200 and 100 students are taking PSYC300.  There are 50 juniors taking both courses.

 

12.    What is the probability that a randomly selected junior is in neither of the two classes? (10 pts)

 

 

                                                                                                                                                                                                      ____________

 

13.    What is the probability that a randomly selected junior takes only one of the two classes? (10 pts)

 

 

                                                                                                                                                                                                      _____________

Refer to the following information for Questions 14 and 15.

 

School STAT CLUB must appoint a Present, a Vice Present, and a Treasurer. It must also select three members for the STAT Olympics team. There are 10 qualified candidates, and appointed officers can also be on the STAT Olympics team.

 

14.    How many different ways can the officers be appointed? (10 pts)

 

                                                                                                                                                                                                      _____________

 

15.  How many different ways can the STAT Olympics team be selected? (10 pts)

 

                                                                                                                                                                                                      _____________

 

Questions 16 and 17 involve the random variable x with probability distribution given below.

Show all work.

 

X

-1

0

1

2

5

P(x)

0.1

0.1

0.4

0.1

0.3

                                   

16.    Determine the expected value of x. (5 pts)

 

                                                                                                                                                                                                      _____________

 

17.   Determine the standard deviation of x.  (Round the answer to two decimal places.) (10 pts)

 

 

                                                                                                                                                                                                      _____________

Consider the following situation for Questions 18, 19 and 20.

 

Mimi made random guesses at 5 true-or-false questions in a STAT 200 pop quiz.  Let random number X be the number of correct answers Mini got.  As we know, the distribution of X is a binomial probability distribution.  Please answer the following questions.

 

18.           What is the number of trials (n)? (2pts)

                                                                                                                                                                                                      _____________

What is the probability of success (p)? (2pts)

                                                                                                                                                                                                      _____________

What is the probability of failure (q)? (1pts)

                                                                                                                                                                                           _____________

19.           Find the probability that she got at least 3 correct answers. (10 pts)

 

 

                                                                                                                                                                                                                                                                                                                                                                                                                                                _____________   

20.           What is the mean of the distribution? (5pts)

 

 

                                                                                                                                                                                                      _____________

 

What is the standard deviation? (Round the answer to two decimal places.)  (5pts)

 

 

                                                                                                                                                                                                      _____________

 

Refer to the following information for Questions 21, 22, and 23.

 

The heights of dogwood trees are normally distributed with a mean of 9 feet and a standard deviation of 3 feet.

 

21.           What is the probability that a randomly selected dogwood tree is between 6 and 15 feet tall?

(10 pts)

 

 

                                                                                                                                                                                                      _____________

22.           Find the 80th percentile of the dogwood tree height distribution. (5 pts)

 

 

 

                                                                                                                                                                                                      _____________

23.           If a random sample of 144 dogwood trees is selected, what is the standard deviation of the sample mean? (5 pts)

 

 

 

                                                                                                                                                                                                      _____________

 

24.           A random sample of 100 GMAT scores has a mean of 500.  Assume that GMAT scores have a population standard deviation of 120.  Construct a 95% confidence interval estimate of the mean GMAT scores.  (15 pts)

 

What is the sample size for the conference interval?

 

 

                                                                                                                                                ____________

 

What is the point estimate for the conference interval?

 

 

                                                                                                                                                ____________

 

                                                      The appropriate distribution for calculating the confidence Interval is:

                                                                                                           

                                                                                          z distribution     t distribution,    Chi Square,          Uniform

 

What is the numerical value of the variable from the above distribution?

 

 

 

                                                                                                                                                _____________

 

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

 

 

 

                                                                                                                                                ___________                           ___________        


 

25.           Given a sample size of 100, with sample mean of 730 and a sample deviation of 100, we perform the following hypothesis test at α = 0.05 level. (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,             Uniform

 

 

Determine the test statistic.  Show or explain how you obtained or calculated the test statistic.

 

 

                                                                                                                                                                                    ____________

 

Determine the critical value.  Explain how you obtained the critical value.

 

                                                                                                                                                                                    ____________

 

 

Is there sufficient evidence to justify the rejection of Ho at α= 0.05 level?

 

a)   No.  There is insufficient evidence to reject the Null Hypothesis.

b)  Yes. There is sufficient evidence to reject the Null Hypothesis.

c)  There is insufficient evidence to make a decision.

 

Explain your answer by finishing the following sentence:

 

The decision for this test is (a, b, or c from above) because the test statistic is  ______________.

 


 

26.           Consider the Hypothesis test given by

 

                  Ho: p = 0.5

                  H1: p > 0.5

 

In a random sample of 225 subjects, the sample proportion is found to be 0.55.

 

What is the appropriate distribution for performing this Hypothesis test?

 

Z distribution,             t distribution,                  Chi Square distribution,             Uniform

 

                 

 

Determine the test statistic.  Show or explain how you obtained or calculated the test statistic.

 

                                                                                                                                                                                                      ____________

 

Determine the Pvalue for this test?  Show or explain how you obtained or calculated the Pvalue.

 

                                                                                                                                                                                                      ____________

 

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

 

a)     Yes there is sufficient evidence to reject the Null Hypothesis.

b)     No there is insufficient evidence to reject the Null Hypothesis.

c)     There is insufficient information to make a decision.

 

Explain your answer by finishing the following sentence:

 

The decision for this test is (a, b, or c from above) because the Pvalue is ____________________.

 

 


 

27.           In a study of memory recall, 5 people were given 10 minutes to memorize a list of 20 words.  Each was asked to list as many of the words as he or she could remember 1 hour and 24 hours later.  The result is shown in the following table.

 

 

Number of Words Recalled

Subject

1 hour later

24 hours later

1

14

10

2

18

14

3

11

9

4

16

12

5

15

12

 

Is there evidence to suggest that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours by more than 3? (30pts)

 

Assume we want to use a 0.01 significance level to test the claim.

 

Identify the null hypothesis.

a)     The difference between the memory recall after 1 hour is 3 greater than the memory recall after 24 hours.

b)     The difference between the memory recall after 1 hour exceed the memory recall after 24 hours by more than 3.

 

 

Identify the alternate hypothesis.

a.     The difference between the memory recall after 1 hour is 3 greater than the memory recall after 24 hours.

b.     The difference between the memory recall after 1 hour exceeds the memory recall after 24 hours by more than 3.

 

 

Determine the test statistic.  Show or explain how you obtained or calculated the test statistic.

 

 

 

 

                                                                                                                                                                  ____________

 

Determine the critical value.  Explain how you obtained the critical value.

 

 

 

 

                                                                                                                                                         ____________

Is there sufficient evidence to support the alternate hypothesis?

 

a.     No    There is insufficient evidence to reject the Null Hypothesis.

b.     Yes   There is sufficient evidence to reject the Null Hypothesis

c.     There is insufficient information to make a decision.

 

Explain your answer by finishing the following sentence:

 

The decision for this test is (a, b, or c from above) because the test statistic is ______________.

 

 

Refer to the following data for Questions 28 and 29.

 

X

0

– 1

3

2

5

Y

3

– 2

3

6

8

                           

 

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?

 

 

                                                                                                                                                                  _____________

 

Fill in the blanks for the regression equation.

                                                                                                                                                       Y = ____   +   _____x

 

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

 

 

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

 

29.           Based on the equation from # 28 what is the predicted value of y if x=4? (10 pts)

 

 

                                                                                                                                                                                                      ___________

 

30.           The School Bookstore sells three different types of coffee mugs. The manager reported that the three types are purchased in proportions: 50%, 30%, and 20%, respectively.   Suppose that a sample of 100 purchases yields observed counts of 46, 28, and 26 for types 1, 2, and 3 respectively

Type

1

2

3

Observed

46

28

26

 

Assume we want to use a 0.10 significant level to test the claim that the reported proportions are correct. (25 pts)

What is the Null Hypothesis?

 

a)     The coffee mug distribution reported is consistent with the observed data.

b)     The coffee mug distribution reported is inconsistent with the observed data.

                                                                                                                                                                 

What is the Alternate Hypothesis?

 

a)     The coffee mug distribution reported is consistent with the observed data.

b)     The coffee mug distribution reported is inconsistent with the observed data.

                                                                                                                                                                 

Determine the degrees of freedom for this Chi Square Hypothesis test?

 

                                                                                                                                                                  __________________

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

 

                                                                                                                                                                  __________________

What is the Chi Square Critical Value?

 

                                                                                                                                                                  __________________

 

Is there sufficient evidence to support the claim that the mug distribution is correct at an alpha of 0.10?

 

a)     No.  There is insufficient evidence to reject the Null Hypothesis (Ho) at an alpha level of 0.10

The data is consistent with the reported mug distribution.

 

b)     Yes.  There is sufficient evidence to reject the Null Hypothesis (Ho) at an alpha level of 0.10.               The data is inconsistent with the reported mug distribution.

 

c)     The test results are inconclusive and we cannot make a decision.

 

 

 

31.           Example question

 

Please note:  Each time you re-do the Final Exam the answer to question 31 may change, but  the subject matter and format of the question will not change.  All of the other questions on the Final Exam will remain the same each time you re-do the Final Exam.

 

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

 

A man is selected by a marketing company to participate in a paid focus group. The company says that the man was selected because everyone in three randomly selected towns was being selected.

 

What type of sampling did the tax department use?

 

Convenience sampling

Random sampling

Cluster sampling

Stratified sampling

Systematic sampling 

Subject Mathematics
Due By (Pacific Time) 10/11/2014 09:00 pm
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