MS 150 Statistics spring 2008 mx • Name:
Part I: Basic statistics, frequencies, histogram, z-scores, normal distribution.
The pedometer data in the table was gathered by the instructor between 20 January and 02 February 2008
- __________ What level of measurement is the data?
- __________ Find the sample size n for the data.
- __________ Find the minimum.
- __________ Find the maximum.
- __________ Find the range.
- __________ Find the median.
- __________ Find the mode.
- __________ Find the sample mean x.
- __________ Find the sample standard deviation sx.
- __________ Find the sample coefficient of variation CV.
- __________ If this data were to be divided into five bins, what would be the width of a single bin?
- Determine the frequency and calculate the relative frequency using five bins. Record your results in the table provided.
|Temperature bins (x)||Frequency (f)||Rel. Freq. p(x)|
- Sketch a histogram chart of the data anywhere it fits, labeling your horizontal axis and vertical axis as appropriate.
- ____________________ What is the shape of the distribution?
- p(x < 4040) = ____________________ What is the probability I will walk 4040 steps or less per day?
- p(x > 9960) = ____________________ The goal of the 10000 step program is to walk 10000 steps per day. What is the probability that I will walk greater than 9960 steps or more per day?
- ____________________ Use the sample mean x and standard deviation sx calculated above to determine the z-score for a day with 10000 steps
- ____________________ Is the z-score for a 10000 step day an ordinary or unusual z-score?
Part II: Linear regression
Pohnpei public health has been handing out pedometers provided by the Pacific Diabetes Education Program through a grant from Imi Hale. The FSM Department of Health has recently received pedometers from WHO. The WHO pedometers use a different mechanism and algorithm than the Imi Hale pedometers. Trials in which both pedometers were worn at the same time provided the data in the accompanying table.
- __________ Does the relationship appear to be linear, non-linear, or random?
- __________ Calculate the slope of the linear regression line for the data.
- __________ Calculate the y-intercept of the linear regression for the data.
- __________ Is the correlation positive, negative, or neutral?
- __________ Determine the correlation coefficient r.
- __________ What is the strength of the correlation?
- __________ Determine the coefficient of determination r² .
- __________ If the Imi Hale pedometer has recorded 450 steps, what is the predicted WHO pedometer step count?
- __________ If the WHO pedometer has recorded 250 steps, what is the predicted Imi Hale pedometer step count?
Table of basic statistical functions used by OpenOffice
|Statistic or Parameter||Symbol||Equations||OpenOffice|
|Sample standard deviation||sx||=STDEV(data)|
|Sample Coefficient of Variation||CV||sx/
|Calculate a z value from an x||z||=
Linear regression functions used by OpenOffice.org
|Slope||b||=SLOPE(y data;x data)|
|Intercept||a||=INTERCEPT(y data;x data)|
|Correlation||r||=CORREL(y data;x data)|
|Coefficient of Determination||r²||
||=(CORREL(y data;x data))^2