Review Materials for Midterm 1

 

Exam coverage: Chapter 1, Chapter 2, Chapter 3.1-3.5, Chapter 4 (but not 4.4), Chapter 5

 

Suggested Extra Problems From Your Textbook:

 

Chapter 3:

Exercise Set A #3, #4, #7

Exercise Set D #2

Review Exercises #1 and #4

 

Chapter 4:

Exercise Set A: #9

Exercise Set B: #1 - #5

Exercise Set E: #1, #4

 

Read the technical note on page 74 and Using a Statistical Calculator (if it applies to you)

 

Chapter 5:

Exercise Set A #1

Exercise Set B #3, #4

Exercise Set C #1

Exercise Set E # 1 and #2

Exercise Set F #1

 

Page 428. #1, #3 (a & b), #5

 

Page 568. #4, #6

 

Relevant Concepts & Statistics

 

Treatment, Treatment Group, Control Group

Response

Confounding, Confounder

Randomization, Randomized Controlled Experiment

Blind, Double-Blind, Placebo

Observational Study

Association

Causation

Histogram, class interval

Variable

Average (mean), Standard Deviation, Median, Minimum, Maximum, Range, 25th Percentile, Median, 75th Percentile, Inter-Quartile Range

Standard Normal Distribution

Z scores or Standard Units

Percentiles and Transforming data or scores

I've asked you to help me select a gift for my financial advisor, I'll call him Oracle.  You know nothing about cigars (I hope) and have some information below from the pages of Cigar Aficionado, a magazine for cigar lovers which provides ratings of various cigars.  Cigars are rated from a scale of 0 (horrible) to 5 (the best) by a panel of cigar experts. 

 

Cigar

Rater 1

Rater 2

Rater 3

Rater4

Rater 5

Rater 6

Hinds

3.9

3.6

3.5

3.5

3.6

3.3

AZ

4.8

2.5

3.9

3.4

3.1

3.7

 

Both cigars cost exactly the same amount per cigar and both are coronas (his favorite) so cost and type of cigar are not issues here.  What is at issue is pleasing Oracle by giving him a cigar that he will probably enjoy.

 

1.  Please calculate the mean, standard deviation, median, and interquartile range of the ratings for each of the cigars. (MAKE SURE YOU FILL OUT THE ANSWER SHEET IN BACK)

(SHOWING WORK IS NOT REQUIRED FOR THIS QUESTION)

 

Hinds

AZ

Mean (1 pt each)

 

 

 

Standard  (2 pts each)

Deviation

 

 

Median (1 pt each)

 

 

 

Interquartile  (2 pts each)

Range

 

 

 

2.  Based on what you have learned about statistics so far, which cigar (I will only buy one) will you advise me to buy for Oracle ? Please explain your choice in terms of the statistics you calculated in the previous problem and from the original Cigar Aficionado ratings if necessary to help your argument. (8 points)

 

 

 

 

Please answer some questions about this graphic.  It was drawn to represent the distribution of returns for a database of mutual funds:

. 

 

 

            3

 

Text Box: % per % return            2.5

 

2

 

1.5

 

1

 

0.5

 

0

                         10       20        30        40      50        60       70       80       90        100

                        (percentage return)

 

 

3.       Using information from the graphic, what is the median percentage return? (5 points)

 

A.        50%

B.                 52.5%

C.                 55%

D.                 This "histogram" has been incorrectly drawn.  The median cannot be determined.

E.                  This "histogram" has been correctly drawn, but the median cannot be determined from a graphic.

 

 

 

4.       What is the inter-quartile range (IQR) of this distribution of mutual fund percentage returns? (5 points)

 

A.  45%

B.     50%

C.     55%

D.     This "histogram" has been incorrectly drawn.  The IQR cannot be determined.

E.   This "histogram" has been correctly drawn, but the IQR cannot be determined from a

      graphic.

 

 

 

 

5. (5 points) A sociologist conducted a study on the effects of two teaching styles. One style was Authoritarian (A) with strict discipline and many rules. The other style was more Democratic (D) where students were given fewer restrictions and encouraged to set their own standards of conduct. Comparing standardized tests scores before and after the teaching techniques were introduced, she found the following:

ALL STUDENTS

STYLE

Number Improved

Number Unimproved

Total

% Improved

D

252

148

400

63%

A

210

190

400

53%

 

When she disaggregated the data into class in school, that is: Freshmen and Sophomores versus Juniors and Seniors she was surprised to see the following:

 

FRESHMEN AND SOPHOMORES

TEACHING STYLE

Number Improved

Number Unimproved

Total

% Improved

D

210

90

300

70%

A

75

25

100

75%

 

JUNIORS AND SENIORS

TEACHING STYLE

Number Improved

Number Unimproved

Total

% Improved

D

42

58

100

42%

A

135

165

300

45%

 

Which is the confounding variable?

A.        Teaching Style

B.         Class in School

C.         Percentage Improved (far right column)

D.        None of the above, there is no confounding in these tables


Al and Larry are mutual fund managers.   Al's fund FEDCHAIR has a one-year return of 

-4% (a loss).   Larry's fund TREASECT has a one-year return of 8% (a gain). The 6,000 mutual funds reported by the Wall Street Journal are normally distributed with a mean one-year return of -1% and a standard deviation of 12%

 

6.         What percentage of mutual funds had returns between Al's & Larry's funds?(5 points)

 

            A.        About 20%

            B.         About 35%

            C.         About 37%

            D.        About 55%

            E.         About 74%

 

7.         Another manager's, Stuart, fund is in the bottom 5% (i.e. about 5% of the funds have returns lower than his) of all mutual funds, what was his one-year return? (5 points)

 

            A.        About -23%

            B.         About -22%

            C.         About -20%

            D.        About -18%

            E.         About -2%

 

8.         In order to meet my retirement goals, I need to buy into a mutual fund that has a return of 14% or more.  Approximately how many funds can I pick from? (5 points)

 

            A.        Less than 650 funds

            B.         About 815 funds

C.         About 840 funds

            D.        About 880 funds

            E.         About 1,270 funds

 

9.         Oracle, my financial adviser, believes inflation should be taken into account when measuring fund performance.  Suppose Oracle adjusts all of the fund returns by subtracting 4% and then multiplying by 2. For example, Al's fund would now return -16% (a loss) according to Oracle.  I need a return of 8% or more now. What percentage of funds qualify? (5 points)

 

            A.        Less than 10%

            B.         Around 25%

C.         More than 50%

            D.        Oracle's formula contains an error, percentage cannot be calculated

E.            Oracle's formula does not contain an error, but there is not enough

information available to calculate a percentage.


10. This graphic appeared in The Daily Bruin last week.  These are some results from a national survey of college freshmen.  Approximately 364,546 freshmen responded and it was statistically adjusted to be representative of the 1.6 million freshmen entering college in the fall of 1999 as first-time, full-time students.  Many questions are asked of the freshmen such as career goals, general levels of satisfaction, drug use, and activity levels.  The article went on to note that stress levels were the highest in 30 years as was the level of those interested in teaching as a career.


 


An unnamed politician reviewed this study and concluded "high stress is good for students because it encourages them to go into teaching as a career and this country needs more teachers."

 

In light of what you have learned so far in Statistics 10 please comment on the politician's analysis of the survey results.  Do you think his conclusions are reasonable?  If yes, please explain why, if not, please tell us why not. (5 points)