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Topic: First Test- Workshop Stat - Unit One
Replies: 1   Last Post: Oct 8, 1996 2:08 PM

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Al Coons

Posts: 898
Registered: 12/4/04
First Test- Workshop Stat - Unit One
Posted: Sep 29, 1996 12:55 PM
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Attached is my first test on Unit One of Workshop Statistics. It was taken
in a 80 minute period. It was long - most students using much of the time.
Tried to grade as many problems as possible hollistically - hard work but
worth it.

What do you think? Would love candid answers.

Al

Albert Coons
Mathematics Department
Buckingham Browne & Nichols School
Gerry's Landing Road
Cambridge, MA 02138
(617) 547-6100
AlCoons@aol.com
9/26/96 AP Statistics - Test 1 - Unit 1 - Topics 1-5 Mr. Coons

1. Two machines, C1 and C2, are making pins which must have a diameter of 8 cm ± 1 cm or they are rejected. Dotplots of 50 pins from each machine are displayed below. They are both on the same scale as marked.


:. . ... ::
: : . .:. ::.: :.:::.::.. : . . . .
+---------+---------+---------+---------+---------+-C1
.
:
:
. :: .
.::::..:.
. .. ::::::::::.: .
+---------+---------+---------+---------+---------+-C2
6.0 7.0 8.0 9.0 10.0 11.0



Estimating by simply looking at the dotplots, i.e. without doing any calculations or counting, fill in the chart below with comparisons between C1 and C2 of "the six features that are often of interest when analyzing a distribution of data."

2. Mayors of some towns will do anything to show how affluent their towns are. Describe how an unscrupulous Mayor might "lie with statistics" by using certain centers for the data which describe the value the homes in his town. Describe any assumptions you have made about the distribution of the data in your answer.


3. Create a data set in which the mean is at least 6 times greater than the median.


4. Two additional numerical measures of the center of a distribution are:

midrange: the average of the minimum and the maximum of its five number summary.
midhinge: the average of the lower and upper quartiles.

Which, if any, of these measures is resistant? Clearly explain what the measure is resistant to and why.

5. The following data is a sorted version of Henry Cavendish's 29 measurements of the density of the earth, made in 17981. It is stored in the TI-83 program EARDEN in the variable DEN.

4.88 5.07 5.10 5.26 5.27 5.29 5.29 5.30 5.34 5.34 5.36 5.39
5.42 5.44 5.46 5.47 5.50 5.53 5.55 5.57 5.58 5.61 5.62 5.63
5.65 5.68 5.75 5.79 5.85

5a) Sketch a very rough copy of an appropriate TI-83 visual display of the distribution, and then state all features of the graph which suggest you either could or could not apply the empirical rule to this distribution.

5b) How well does this data fit the Empirical Rule for two standard deviations? Clearly support your work.

5c) Assume this data is typical of the data obtained from any 29 samples of earth. Use the empirical rule to predict the smallest theoretical density of the earth which is greater than about 84% of the data in 29 new samples. Show your calculation.

5d) This is very old data, taken in 1798 (From BPS, pg 75, Exercise 1.53). Let's assume that Cavendish worried about the accuracy of his experiments:
i) Showing your calculations clearly, determine if there are any outliers in the data.
ii) Having completed part a), make a statement about the accuracy of Cavendish's work. Make sure you are not misleading and that you cover any assumptions.

6. The Commonwealth of Massachusetts has taken BADCO, a major company, to court on allegations that it discriminates against women by not paying equal wages for equal work. Who would use the chart to the right in their arguments (NOTE: TWO BOX PLOTS WITH MAX OF EACH SIMILAR, MEDIAN OF FEMALES BELOW Q1 OF MALES, MINIMUM OF MALES BETWEEN Q1 AND MEDIAN OF FEMALES)

a) the lawyers for BADCO, or
b) The Commonwealth of Massachusetts? 

What would they say to the jury in explaining what the chart shows? Assume the jury has no statistical background and begins to fall asleep as soon as they have to listen to details.

7. Three data values are described by x, x + 17, and x + 34 where x is any number. Calculate the standard deviation of this data without using the statistics functions of your calculator. Clearly show your work.

8. Given any data set of n measurement variables x1, x2, x3, ..., xn . What is the effect on the standard deviation if the same constant is subtracted from each value. Prove your conjecture in a convincing way. This proof might or might not involve traditional mathematics computations.





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