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Assignment Handout
Introduction
Kelley and Mike are planning on moving to Chardon, Ohio (41º 34’ 45” North, 81º 12’ 16” West). Chardon is the
seat of Geauga County and is the snowbelt capital of Northeastern Ohio. The city’s website
(http://www.chardon.cc/textdocuments/snow.htm) includes historical snowfall (updated monthly) going back to
1952. Kelley and Mike want to know the normal yearly (or mean) snowfall of Chardon.
Part I
Mike believes that he can answer their question by taking any ten consecutive years from the sample data set and
calculate their mean. He decides to begin with the __________ year (this will be provided by your instructor). In
order to gain more information Mike also calculates the standard deviation for these years. Use this information to
complete page 2 of this handout.
Part II
After looking at the list of historical data, Kelley doesn’t think that Mike’s approach correctly answers their
question. She uses the entire sample data set and calculates a __________% confidence interval (this will be
provided by your instructor). Instead of using the traditional standard deviation formula she decides to use a shortcut formula. Use this information to complete pages 3 and 4 of this handout.
Summary
Briefly summarize this assignment on page 5 of this handout. What does Kelley’s confidence interval tell us? How
does Mike’s results compare to Kelley’s results? What surprised you?
1
Mike’s Result
Mike believes that he can answer their question by taking any ten consecutive years from the data set and calculate
their mean. He decides to begin with the __________ year (this will be provided by your instructor). In order to
gain more information Mike also calculates the standard deviation for these years.
YEAR
SNOWFALL (X)
(X – MEAN)2
X - MEAN
TOTALS
Steps
(1)
Beginning with the year given by your instructor, list the years and snowfalls in the first two columns
above.
(2)
Add up the “Snowfall” (second) column and place this value at the bottom of the column.
(3)
Calculate the mean of this data set by dividing the answer from step 2 by 10.
Mean 
X
n

TOTAL SNOWFALL

10

10
(4)
In the “X – Mean” (third) column subtract the mean calculated in step 3 from each of the entries in the
“Snowfall” (second) column.
(5)
Add up the “X – Mean” (third) column and place this value at the bottom of the column. This result
should be zero (0). If the result is off by a little it might be due to rounding.
(6)
In the “(X – Mean)2” (fourth) column enter the square of each of the entries of the “X – Mean” (third)
column.
(7)
Add up the “(X – Mean)2” (fourth) column and place this value at the bottom of the column.
(8)
Calculate the standard deviation of this data set by dividing the answer from step 7 by 9 and then
taking the square root of the result.
s
(9)
(X  X )
n 1
2

  X  MEAN 
10  1
2

9


Results – According to Mike’s calculations the mean is __________ and the standard deviation is
__________ (rounded to two decimal places).
2
Kelley’s Result
After looking at the list of historical data, Kelley doesn’t think that Mike’s approach correctly answers their
question. She uses the entire data set and calculates a __________% confidence interval (this will be provided by
your instructor).
Steps
(1)
(2)
(3)
Beginning with the 1952 – 1953 year list the snowfall for each year in the “Snowfall” (second) column
of the table on page 4.
Add up the “Snowfall” (second) column and place this value at the bottom of the column.
Calculate the mean of this data set by dividing the answer from step 2 by 53.
Mean 
(4)
(5)
(6)
X

n
 X 
 X   n
2
s
n 1
s
(8)


 
2
53
53  1
2
53
52

52

Calculate the zα/2 corresponding to your confidence interval. This can be done by dividing the
confidence level (in decimal form) by 2 and then finding it within the standard normal (z) table. The
corresponding z-score is the zα/2. The zα/2 corresponding to our confidence interval is _________.
Calculate the lower limit of our confidence interval by subtracting the product of the standard
deviation (step 6) divided by the square root of 53 and z α/2 from the mean (step 3).
2
s
n

 
 


 
53 
Calculate the upper limit of our confidence interval by adding the product of the standard deviation
(step 6) divided by the square root of 53 and zα/2 to the mean (step 3).
Upper Limit  X  z 
2
(10)

TOTAL COLUMN 3  TOTAL COLUMN 2
Lower Limit  X  z 
(9)
53
In the “Snowfall2” (third) column square each of the entries in the “Snowfall” (second) column.
Add up the “Snowfall2” (third) column and place this value at the bottom of the column.
Calculate the standard deviation of this data set by subtracting the square of the sum of the “Snowfall”
(total from the second column) divided by 53 from the sum of the “Snowfall 2” (total from the third
column), then divide this result by 52, and then finally take the square root of the result.
2
(7)
TOTAL SNOWFALL

53
s
n

 
 


 
53 
The true mean is likely located somewhere between the lower limit and upper limit calculated in steps
8 and 9 respectfully. We can be _____% (same value as given above) sure that the true mean is
between __________ and _________ (rounded to two decimal places).
3
YEAR
1952 - 1953
1953 - 1954
1954 – 1955
1955 – 1956
1956 – 1957
1957 – 1958
1958 – 1959
1959 – 1960
1960 – 1961
1961 – 1962
1962 – 1963
1963 – 1964
1964 – 1965
1965 – 1966
1966 – 1967
1967 – 1968
1968 – 1969
1969 - 1970
1970 – 1971
1971 – 1972
1972 – 1973
1973 – 1974
1974 – 1975
1975 – 1976
1976 – 1977
1977 – 1978
1978 – 1979
1979 – 1980
1980 – 1981
1981 – 1982
1982 – 1983
1983 – 1984
1984 – 1985
1985 – 1986
1986 – 1987
1987 – 1988
1988 – 1989
1989 – 1990
1990 – 1991
1991 – 1992
1992 – 1993
1993 – 1994
1994 – 1995
1995 – 1996
1996 – 1997
1997 – 1998
1998 – 1999
1999 – 2000
2000 – 2001
2001 – 2002
2002 – 2003
2003 - 2004
2004 – 2005
TOTALS
SNOWFALL (X)
4
SNOWFALL2 (X2)
SUMMARY
Briefly summarize this assignment. What does Kelley’s confidence interval tell us? How does Mike’s results
compare to Kelley’s results? What surprised you?
5