NY Marathon 2011 The table below shows the winningtimes (in minutes) for men and women in the New YorkCity Marathon between 1978 and 2011. Assuming thatperformances in the Big Apple resemble performanceselsewhere, we can think of these data as a sample ofperformance in marathon competitions. Create a 90%confidence interval for the mean difference in winningtimes for male and female marathon competitors.(www.nycmarathon.org) Year Men Women Year Men Women1978 132.2 152.5 1995 131.0 148.11979 131.7 147.6 1996 129.9 148.31980 129.7 145.7 1997 128.2 148.71981 128.2 145.5 1998 128.8 145.31982 129.5 147.2 1999 129.2 145.11983 129.0 147.0 2000 130.2 145.81984 134.9 149.5 2001 127.7 144.41985 131.6 148.6 2002 128.1 145.91986 131.1 148.1 2003 130.5 142.51987 131.0 150.3 2004 129.5 143.21988 128.3 148.1 2005 129.5 144.71989 128.0 145.5 2006 130.0 145.11990 132.7 150.8 2007 129.1 143.21991 129.5 147.5 2008 128.7 143.91992 129.5 144.7 2009 129.3 148.91993 130.1 146.4 2010 128.3 148.31994 131.4 147.6 2011 125.1 143.3
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
NY Marathon 2011 The table below shows the winning
times (in minutes) for men and women in the New York
City Marathon between 1978 and 2011. Assuming that
performances in the Big Apple resemble performances
elsewhere, we can think of these data as a sample of
performance in marathon competitions. Create a 90%
confidence interval for the
times for male and female marathon competitors.
(www.nycmarathon.org)
Year Men Women Year Men Women
1978 132.2 152.5 1995 131.0 148.1
1979 131.7 147.6 1996 129.9 148.3
1980 129.7 145.7 1997 128.2 148.7
1981 128.2 145.5 1998 128.8 145.3
1982 129.5 147.2 1999 129.2 145.1
1983 129.0 147.0 2000 130.2 145.8
1984 134.9 149.5 2001 127.7 144.4
1985 131.6 148.6 2002 128.1 145.9
1986 131.1 148.1 2003 130.5 142.5
1987 131.0 150.3 2004 129.5 143.2
1988 128.3 148.1 2005 129.5 144.7
1989 128.0 145.5 2006 130.0 145.1
1990 132.7 150.8 2007 129.1 143.2
1991 129.5 147.5 2008 128.7 143.9
1992 129.5 144.7 2009 129.3 148.9
1993 130.1 146.4 2010 128.3 148.3
1994 131.4 147.6 2011 125.1 143.3
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