MS 150 Statistics Fall 2004 Mx • Name:

On the road!

In an attempt to save some cut and paste time, the data used in this midterm is in a spreadsheet. If viewing this page online, right-click with the right mouse button on the link below and choose "Save target as... to save this file to your computer. The file can then be opened with Excel.
http://www.comfsm.fm/~dleeling/statistics/s43/mdata.xls • html format

Basic statistics, Frequencies, histograms, and Probabilities

Data
Tire pressure/
psi
33
35
31
34
27
25
31
28
30
33
30
31
29
32
28

Under-inflation is not only the tire's enemy for durability but is a significant contributor to increased rolling resistance and loss of fuel economy. Under-inflation by as little as 20% can reduce tire life up to 50% and increase fuel consumption by 3%. Fifteen tires with a recommended air pressure of 35 pounds per square inch (PSI) were randomly measured for their air pressure. The measurements are given in the table.

  1. __________ What level of measurement is tire pressure in pounds per square inch?
  2. __________ Find the sample size n for the tire pressure data.
  3. __________ Find the minimum tire pressure.
  4. __________ Find the maximum tire pressure.
  5. __________ Find the range of the tire pressure.
  6. __________ Find the median tire pressure.
  7. __________ Find the mode for the tire pressure.
  8. __________ Find the sample mean tire pressure.
  9. __________ Find the sample standard deviation for the tire pressure.
  10. __________ Find the sample coefficient of variation CV.
  11. __________ If this data were to be divided into five bins, what would be the width of a single bin?
  12. Determine the frequency and calculate the relative frequency using five bins. Record your results in the table provided.
    Frequency table
    Bins (x)Frequency (f)Rel. Freq. p(x)
    _____________________
    _____________________
    _____________________
    _____________________
    _____________________
    Sum: ______________
  13. Sketch a relative frequency histogram chart of the data here or on the back, labeling your horizontal axis and vertical axis as appropriate.
  14. __________ What is the shape of the distribution?

Calculation of Mean from Frequency Table

Treadwear. In 1973 tire treads lasted for roughly 24,000 miles. Today most passenger car tires average about 41,000 miles before their treads wear out. The United States Department of Transportation rates tires using a grading system. A control tire is assigned a grade of 100. A tire with a grade of 200 can be expected to last twice as long as the control tire, while a tire with a grade of 80 is normally less durable.

The USDOT has data on 2397 tires available on their web site. Use the table below to work out the mean grade for the 2397 tires.

Mean from frequency distribution
Grade binsFreqRF or P(x)x*p(x)
168112____________________
316658____________________
4641172____________________
612332____________________
760123____________________
Sums:_________________________
  1. __________ What is the mean grade for the 2397 tires?

Linear regression

Goodyear P205/70R14 light truck tires are to have their inflation pressure adjusted according to the load. Goodyear provides the following tire load limits (lbs) at the shown cold inflation pressures.

Linear regression
Pressure/PSILoad/lbs
20992
231062
261123
291183
321243
351302
  1. __________ Calculate the slope of the linear trend line (also known as best fit line, least squares, linear regression) for the pressure versus load data.
  2. __________ Calculate the y-intercept for the data.
  3. __________ Is the correlation positive, negative, or neutral?
  4. __________ Determine the correlation coefficient r.
  5. __________ Is the correlation none, low, moderate, high, or perfect?
  6. __________ Does the relationship appear to be linear or non-linear?
  7. __________ Determine the coefficient of determination.
  8. __________ What percent in the variation in pressure variable accounts for the variation in load variable?
  9. __________ Based on the equation of the linear trend line, a tire with an inflation of 25 psi could be expected to bear what load in pounds?
  10. __________ Based on the equation of the linear trend line, a load of 1284 pounds would require what inflation pressure?
  11. __________ Based on the equation of the linear trend line, a tire with an inflation of 100 psi could be expected to bear what load in pounds?

Normal curves

  1. ___ Which of the following curves is a normal curve?
    mx_normal (3K)
  2. For the following normal distribution determine:
    1. ________ What is the mean?
    2. ________ What is the standard deviation?

    mx_normalii (4K)
Table of statistical functions used by Excel
Statistic or Parameter Symbol Equations Excel
Square root =SQRT(number)
Sample mean x Σx/n =AVERAGE(data)
Sample standard deviation sx =STDEV(data)
Sample Coefficient of Variation CV sx/x =STDEV(data)/AVERAGE(data)
Slope b =SLOPE(y data, x data)
Intercept a =INTERCEPT(y data, x data)
Correlation r =CORREL(y data, x data)
Coefficient of Determination rČ =(CORREL(y data, x data))^2