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

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 median.
7. __________ Find the mode.
8. __________ Find the sample mean x.
9. __________ Find the sample standard deviation sx.
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.

13. Sketch a histogram chart of the data anywhere it fits, labeling your horizontal axis and vertical axis as appropriate.
14. ____________________ What is the shape of the distribution?
15. p(x < 4040) = ____________________ What is the probability I will walk 4040 steps or less per day?
16. 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?
17. ____________________ Use the sample mean x and standard deviation sx calculated above to determine the z-score for a day with 10000 steps
18. ____________________ 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.

19. __________ Does the relationship appear to be linear, non-linear, or random?
20. __________ Calculate the slope of the linear regression line for the data.
21. __________ Calculate the y-intercept of the linear regression for the data.
22. __________ Is the correlation positive, negative, or neutral?
23. __________ Determine the correlation coefficient r.
24. __________ What is the strength of the correlation?
25. __________ Determine the coefficient of determination r² .
26. __________ If the Imi Hale pedometer has recorded 450 steps, what is the predicted WHO pedometer step count?
27. __________ 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
Square root	√		=SQRT(number)
Sample size	n		=COUNT(data)
Minimum			=MIN(data)
Maximum			=MAX(data)
Median			=MEDIAN(data)
Mode			=MODE(data)
Sample mean	x	Σx/n	=AVERAGE(data)
Sample standard deviation	sx		=STDEV(data)
Sample Coefficient of Variation	CV	sx/ x	=STDEV(data)/AVERAGE(data)
Calculate a z value from an x	z	=	=STANDARDIZE(x;x;sx)