Question

Please Use R studio and show all the steps to answer this question

NY Marathon 2013 the table below shows the winning times (in minutes) for men and women in the new york city marathon between 1978 and 2013. (the race was not run in 2012 because of superstorm sandy.) 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 mean difference in winning times for male and female marathon competitors.

Year	Men	Women	Year	Men	Women
1978	132.2	152.5	1996	129.9	148.3
1979	131.7	147.6	1997	128.2	148.7
1980	129.7	145.7	1998	128.8	145.3
1981	128.2	145.5	1999	129.2	145.1
1982	129.5	147.2	2000	130.2	145.8
1983	129.0	147.0	2001	127.7	144.4
1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995	134.9 131.6 131.1 131.0 128.3 128.0 132.7 129.5 129.5 130.1 131.4 131.1	149.5 148.6 148.1 150.3 148.1 145.5 150.8 147.5 144.7 146.4 147.6 148.1	2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013	128.1 130.5 129.5 129.5 130.0 129.1 128.7 129.3 128.3 125.1 Cancelled 128.4	145.9 142.5 143.2 144.7 145.1 143.2 143.9 148.9 148.3 143.3 Cancelled 140.1

Answer 1

Result:

Data are paired on year. paired t test command is used to get confidence interval for mean difference.

RStudio code:

men<-c(132.2,131.7,129.7,128.2,129.5,129,134.9,131.6,131.1,131,128.3,128,132.7,129.5,129.5,130.1,131.4,131.1,129.9,128.2,128.8,129.2,130.2,127.7,128.1,130.5,129.5,129.5,130,129.1,128.7,129.3,128.3,125.1,128.4)

women<-c(152.5,147.6,145.7,145.5,147.2,147,149.5,148.6,148.1,150.3,148.1,145.5,150.8,147.5,144.7,146.4,147.6,148.1,148.3,148.7,145.3,145.1,145.8,144.4,145.9,142.5,143.2,144.7,145.1,143.2,143.9,148.9,148.3,143.3,140.1)

t.test(men,women, paired = TRUE,conf.level=0.90)

output:

t.test(men,women, paired = TRUE,conf.level=0.90)

        Paired t-test

data: men and women

t = -46.236, df = 34, p-value < 2.2e-16

alternative hypothesis: true difference in means is not equal to 0

90 percent confidence interval:

-17.39663 -16.16908

sample estimates:

mean of the differences

            -16.78286

90% confidence interval for the mean difference in winning times for male and female marathon competitors= (-17.39663, -16.16908)