9/23/97
AP Statistics - Test 1
Unit 1: Topics 1-5
Mr. Coons

1. Two companies, The Tool Company and The Machine Company, have made prototype devices to automatically throw softballs a fixed distance. Below are the results of 100 throws for each device. Each device was set to throw each ball a distance of 55 feet.

 

a. Fill in the chart below with comparisons of The Tool Company and The Machine Company data for "the six features that are often of interest when analyzing a distribution." Do this by simply looking at the dotplots. Do not do any counting or calculations.

b. Each company argued that its prototype is better. In a sentence or two write what you think each company's argument was?

c. Below Minitab's descriptive statistics for the Machine Company's data. Formally determine if The Machine Company's minimum data value is an outlier. Show your work.

d. Demonstrate your understanding of the empirical rule for three standard deviations by applying it Machine Company's data and explaining whether or not the rule seems to hold reasonably well. You can use the descriptive statistics displayed above. Show your work.

e. Draw, without counting, a very rough boxplot of The Tool Company's data by looking at the dotplot of that data . There is no need to label values or worry about possible outliers, simply make the relative sizes of the parts clear. Careful: do not use the Machine Company's data.

2. A study considers the variable: The weight of an automobile. Circle the true answer:


a) The case of the variable is automobile and it is a measurement variable.
b) The case of the variable is automobile and it is a categorical variable.
c) The case of the variable is weight and it is a measurement variable.
d) The case of the variable is weight and it is a categorical variable.
e) None of the above.

3. Circle the answer in which all entries are resistant statistics [Motivated by questions from Jamie Bard and Brian O'Connor]

a) mode, median, mean
b) Q1, median, Q3, IQR
c) range, mean, standard deviation
d) median, mean
e) none of the above

4. The two boxplots to the right show the distributions of red and orange M&Ms from the 17 bags of M&Ms which were inspected by 1996-7 AP Stats class. Write a paragraph or two to a knowledgeable statistician at The Mars Candy Company explaining what might be expected about the number of red and orange M&Ms in an 18th bag taken from the same stock.

5. The formula for a z-score is
. [Motivated by a question from Mike Dimella]

a. Explain the purpose of z-scores.

b. In detail, explain how the formula actually fulfills your answer in part a.

c. The best male long jumpers for State College since 1973 have averaged a jump of 263.0 inches with a standard deviation of 14.0 inches. The best female long jumpers have averaged 201.2 inches with a standard deviation of 7.7 inches. Which athlete is more impressive within their class, a male with a jump of 275 inches or a female with a jump of 207 inches? Prove your answer with appropriate calculations. [From Bill Harrington, Teacher, State College Area High School, State College, PA]

6. This problem asks you to make a generalization based on the empirical rule:

Assume that after applying the empirical rule to data which forms a mound shaped distribution, about 95% of that data lies between the numbers a and b. Determine a formula for the sample standard deviation of the data in terms of a & b?

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