MS 150 Statistics test three (midterm) • Name:

Time/min
24.5
24.0
27.7
23.6
26.8
26.7
23.5
23.6
27.9
27.2
20.0
25.1
28.2
26.8
27.3
27.3
26.3
27.6
31.9
25.3

Part I: Basic statistics, frequencies, histogram, z-scores.

A standard is merely something against which one measures something. The Dausokele bridge over the Nett River is 3.81 kilometers from where I start my runs. A run out to the east side of the bridge has been a standard distance of mine for the past seven years. The times in the table are in minutes.

  1. __________ What level of measurement is the data?
  2. __________ Find the sample size n for the data.
  3. __________ Find the minimum.
  4. __________ Find the maximum.
  5. __________ Find the range.
  6. __________ Find the midrange.
  7. __________ Find the median.
  8. __________ Find the mode.
  9. __________ Find the sample mean x.
  10. __________ Find the sample standard deviation sx.
  11. __________ Find the sample coefficient of variation CV.
  12. __________ If this data were to be divided into five classes, what would be the width of a single class?
  13. Determine the frequency and calculate the relative frequency using five bins. Record your results in the table provided.
Class upper limitsFrequency (f)Rel. Freq. p(x)
Sum:
  1. Sketch a histogram chart of the data anywhere it fits, labeling your horizontal axis and vertical axis as appropriate.
  2. ____________________ What is the shape of the distribution?
  3. ____________________ Use the sample mean x and standard deviation sx calculated above to determine the z-score for a 20 minute run to the far side of the Nett River bridge.
  4. ____________________ Is the z-score for a 20 minute run an ordinary or unusual z-score?

SVG xy scatter graph major grid lines axes x-axis and y-axis data points as circles linear regression line text layers Date versus time to Dausokele ( Nett Bridge Far Side ) Date Time to or from NBFS y-axis labels 20 21 22 24 25 26 27 28 30 31 32 x-axis labels 11/12/01 7/8/02 3/4/03 10/28/03 6/23/04 2/16/05 10/13/05 6/9/06 2/2/07 9/29/07 5/24/08

Part II: Linear Regression

DateTime to or from NBFS
2/20/0824.5
3/19/0824.0
3/23/0827.7
5/22/0823.6
5/25/0826.8
3/21/0826.7
10/25/0723.5
10/2/0723.6
6/30/0727.9
6/17/0727.2
10/17/0620.0
5/10/0625.1
5/10/0628.2
10/8/0526.8
10/8/0527.3
10/15/0427.3
10/11/0326.3
11/6/0327.6
12/31/0231.9
11/12/0125.3

Again use the data spreadsheet to avoid data entry errors. Note that the dates are simply another number to a spreadsheet. All of the usual functions can be applied.

  1. __________ Does the relationship appear to be linear, non-linear, or random?
  2. __________ Calculate the slope of the linear regression line for the data. Be careful: use format:cells to increase the decimal places to five decimal places and record the slope to five decimal places.
  3. __________ Calculate the y-intercept of the linear regression for the data. Two decimal places are sufficient for the y-intercept.
  4. __________ Is the correlation positive, negative, or neutral?
  5. __________ Am I faster, slower, or staying the same in terms of my time to Nett bridge?
  6. __________ Determine the correlation coefficient r.
  7. __________ What is the strength of the correlation?
  8. __________ Determine the coefficient of determination r² .
  9. __________ Toughie. What is my predicted time to Nett Bridge far side on 1/1/2009? Be careful: use your spreadsheet. Enter the date 1/1/2009 into a cell and calculate the slope-intercept equation using the spreadsheet. Use "point=and-click" to calculate the result. You can NOT get this one right using a calculator. Your answer should "make sense" - it should be a time that it would appear I could actually achieve!
  10. Discuss whether predictions can or cannot be accurately made based on the correlation.

MS 100 College Algebra • MS 150 Statistics • Courses • COMFSM