Elements of Statistics (Math 6) - Exam 1
September 27, 1995 - Hartlaub

Directions: Please answer all of the questions below. The point values for each problem are indicated in parentheses. Partial credit will be awarded if you show your work.

1. The September 24, 1995 issue of The Columbus Dispatch contained residential listings of all homes for sale in the Columbus area. The file p:\data\math\stats\homes.mtw contains the prices of homes listed with the HER realtor. Retrieve the file and answer the questions below.

(5) a. Is the distribution of home prices symmetric or skewed?

(6) b. List two measures of center for the prices of homes listed with HER.

(6) c. List two measures of spread for the prices of homes listed with HER.

(5) d. Which measure of spread do you prefer for this data? Provide a short rationale for your choice.

(5) e. Construct a normal probability plot and comment on whether or not you would be willing to use the normal model for this data.

(6) f. Recall that linear transformations are defined by x^* = a + bx. Give the values of a and b that would be used to transform the selling price in dollars, x, to the selling price in thousands of dollars, x^*.

(5) g. Suppose a real estate agent sells five homes in a month and the average price of the homes sold is $195,000. If the agent works strictly on commission and makes 3% of her total sales for the month, can you find the gross amount of her paycheck for this month?

2. Suppose that high school grade point averages for the class of 2000 are normally distributed with a mean of 3.3 and a standard deviation of 0.3.

(5) a. What percent of the students in the class of 2000 have gpa's below 2.7?

(5) b. How high must a student's gpa be for them to place in the top 5% of the class?

(5) c. What percent of the students in the class of 2000 have gpa's above 3.5?

(5) d. How low must a student's gpa be for them to place in the bottom 20% of the class?

(5) e. What percent of the students in the class of 2000 have gpa's between 2.85 and 3.65?

3. The file p:\data\math\stats\examsm6.mtw contains exams scores for Kenyon students enrolled in Math 6 several years ago. Column 1 contains scores on the second exam and column 2 contains scores on the final exam. Usually in the last week of classes many students approach me and ask me to predict (or help them predict) their grade on the final exam and their grade for the course. Retrieve the file and answer the questions below.

(5) a. Is the association between exam 2 scores and final exam scores positive or negative?

(3) b. Find the value of the correlation coefficient.

(6) c Find the least squares regression line for predicting final exam scores.

(3) d. Predict the final exam score for a student who received an 82 on exam 2.

(3) e. What is the value of the residual for the student who received an 86 on exam 2 and a 68.97 on the final exam?

(5) f. Does the least squares line do a "good" job at predicting final exam scores for the students in this course? Please explain in a sentence or two.

4.(20) Carefully describe how the standard deviation measures variability in a set of data. Your description should include the relationship between the sample variance and the standard deviation.

1. (10) A student with an IQ of 140 claims that her IQ score is in the top 5% of the students at her University. Is her claim true if IQ scores are normally distributed at her university, with a mean of 125 and a standard deviation of 10? (Justify your answer to receive full credit.)

2. (10) Two holes are made in a sheet of metal for the insertion of a two-pronged plug in an assembly process. The holes can be anywhere from 0.67 to 0.71 inches apart and the plug will still fit. If the distance between holes is normally distributed with a mean of 0.68 inches and a standard deviation of 0.01, find the proportion of metal sheets that the plugs will not fit. (Justify your answer to receive full credit.)

3. (5) Consider picking 12 numbers from the whole numbers 1 to 12, with repeats allowed. Pick 12 numbers that have the largest possible standard deviation. Can you find another set of 12 numbers with this same value of s?

4. (10) Explain the difference between positive association and negative association in two quantitative variables. Your explanation should be concise and to the point.

5. On Feb. 11, 1992, President Bush stated that the United States would phase out production of ozone-damaging chemicals, mainly chlorofluorocarbons (CFCs), by the end of 1995. In response to the call to eliminate CFCs, a major electronics manufacturer has developed a new low-residue soldering process that eliminates the need to use CFCs. In order to have the new process accepted for widespread use, the manufacturer must prove that it produces high-quality solder joints. A mechanical pull strength is one way to determine the quality of the solder joints. More specifically, two identical pins are soldered on each of several printed wiring boards to determine the strength of the solder joints. One pin is soldered on the left-hand side of the board and the other on the right-hand side. After two weeks of environmental conditioning, the pins are pulled from the board. The pull strengths (in pounds) have been entered into the Minitab worksheet p:\data\math\stats\pins.mtw. Retrieve this worksheet and answer the questions below.

a. (5) List two measures of center for the pull strengths of the left pin.

b. (5) List two measures of spread for the pull strengths of the right pin.

c. (10) Display the data using boxplots or histograms. Do the graphs indicate any difference in the pull strengths for the two different positions on the wiring board?

d. (10) Identify the 5 values that are used to construct the boxplot for the pull strengths of the left pin.

e. (10) You are told to assume that the pull strengths of the right pin follow the normal distribution. Is this a reasonable assumption? State the method you are using to check normality and give a brief justification (one or two sentences) of your answer.

f. (10) Suppose you are presenting these results to a friend in England who is not familiar with the pound as a unit of measurement. Specify the sample mean, median, standard deviation, and interquartile range for the pull strengths of the left pin in kilograms (kg).