MS 150 Statistics Spring 2005 Mx • Name:

Landis+Gyr Cash Power!

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/s51/mdata.xls

Basic statistics, frequencies, and histogram

Data
KwH
9.2
11.3
11
8.4
9.4
8
10.3
9.4
8.9
9.6
7.7
12.4
9.1
9.4
7
9.1
11.6
7.7
10.3
9.7

The utilities corporations in the FSM are moving all of their customers to cash power. Pohnpei Utility Corporation began the transition to Cash Power because the amount of money owed to the utility by customers had reached half a million dollars. With a prepaid power system such as Cash Power, the utility hopes to eliminate such losses going forward. Landis+Gyr of South Africa also notes that Cash Power appears to help and encourage consumers to conserve power. The data is the daily usage in kilowatt-hours in the instructor's home over a period of twenty days.

  1. __________ What level of measurement is kilowatt-hours?
  2. __________ Find the sample size n for the kilowatt-hours data.
  3. __________ Find the minimum kilowatt-hours.
  4. __________ Find the maximum kilowatt-hours.
  5. __________ Find the range of the kilowatt-hours.
  6. __________ Find the median kilowatt-hours.
  7. __________ Find the mode for the kilowatt-hours.
  8. __________ Find the sample mean kilowatt-hours.
  9. __________ Find the sample standard deviation for the kilowatt-hours.
  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

Average cost. Over a period of forty days the instructor tracked the daily power usage and then used the current price of $3.99 KwH per dollar to determine the cost per day for power in the instructor's home. Use the following data collected during a 40 day period this spring to determine the mean cost of power per day in the instructor's home.

Daily cost distribution
Cost bins/$ (x)FreqRF or p(x)x*p(x)
1.8640.10__________
2.18130.325__________
2.49100.25__________
2.8080.20__________
3.1150.125__________
Sums:401.00__________
  1. __________ What is the mean cost per day?

Binomial Expected Outcome

  1. __________ A substance abuse survey found that p = 0.76 of a sample consisting of statistics students chew betelnut. Use N = 801 to estimate the expected number of betelnut chewers in the campus population.

Linear regression

The following table contains a week of Cash Power meter readings from Sunday (day 1) to Saturday (day 7). Use the data in the x and y columns to

Linear regression
Weekday (x)Remaining balance/KwH (y)
1142
2130
3123
4114
5102
694
784
  1. __________ Calculate the slope of the linear trend line (also known as best fit line, least squares, linear regression) for the weekday versus remaining balance 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 weekday accounts for the variation in the remaining balance variable?
  9. __________ Presume power consumption continues at a linear rate beyond the seventh day for the following questions. Based on the equation of the linear trend line, what will be the balance on day ten?
  10. __________ Based on the equation of the linear trend line, on what day will the remaining balance be 50 (and the frowny face will light up red!)?
  11. __________ Based on the equation of the linear trend line, on what day will the remaining balance be 0 (and the power will go off!)?
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)
Binomial distribution expected outcome ” np =n*p
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