Sex Wt 1 1 789 2 1 744 3 1 691 4 1 749 5 1 646 6 1 637 7 1 7

\"Sex\" \"Wt\"

\"1\" 1 78.9

\"2\" 1 74.4

\"3\" 1 69.1

\"4\" 1 74.9

\"5\" 1 64.6

\"6\" 1 63.7

\"7\" 1 75.2

\"8\" 1 62.3

\"9\" 1 66.5

\"10\" 1 62.9

\"11\" 1 96.3

\"12\" 1 75.5

\"13\" 1 63

\"14\" 1 80.5

\"15\" 1 71.3

\"16\" 1 70.5

\"17\" 1 73.2

\"18\" 1 68.7

\"19\" 1 80.5

\"20\" 1 72.9

\"21\" 1 74.5

\"22\" 1 75.4

\"23\" 1 69.5

\"24\" 1 66.4

\"25\" 1 79.7

\"26\" 1 73.6

\"27\" 1 78.7

\"28\" 1 75

\"29\" 1 49.8

\"30\" 1 67.2

\"31\" 1 66

\"32\" 1 74.3

\"33\" 1 78.1

\"34\" 1 79.5

\"35\" 1 78.5

\"36\" 1 59.9

\"37\" 1 63

\"38\" 1 66.3

\"39\" 1 60.7

\"40\" 1 72.9

\"41\" 1 67.9

\"42\" 1 67.5

\"43\" 1 74.1

\"44\" 1 68.2

\"45\" 1 68.8

\"46\" 1 75.3

\"47\" 1 67.4

\"48\" 1 70

\"49\" 1 74

\"50\" 1 51.9

\"51\" 1 74.1

\"52\" 1 74.3

\"53\" 1 77.8

\"54\" 1 66.9

\"55\" 1 83.8

\"56\" 1 82.9

\"57\" 1 64.1

\"58\" 1 68.85

\"59\" 1 64.8

\"60\" 1 59

\"61\" 1 72.1

\"62\" 1 75.6

\"63\" 1 71.4

\"64\" 1 69.7

\"65\" 1 63.9

\"66\" 1 55.1

\"67\" 1 60

\"68\" 1 58

\"69\" 1 64.7

\"70\" 1 87.5

\"71\" 1 78.9

\"72\" 1 83.9

\"73\" 1 82.8

\"74\" 1 74.4

\"75\" 1 94.8

\"76\" 1 49.2

\"77\" 1 61.9

\"78\" 1 53.6

\"79\" 1 63.7

\"80\" 1 52.8

\"81\" 1 65.2

\"82\" 1 50.9

\"83\" 1 57.3

\"84\" 1 60

\"85\" 1 60.1

\"86\" 1 52.5

\"87\" 1 59.7

\"88\" 1 57.3

\"89\" 1 59.6

\"90\" 1 71.5

\"91\" 1 69.7

\"92\" 1 56.1

\"93\" 1 61.1

\"94\" 1 47.4

\"95\" 1 56

\"96\" 1 45.8

\"97\" 1 47.8

\"98\" 1 43.8

\"99\" 1 37.8

\"100\" 1 45.1

\"101\" 0 67

\"102\" 0 74.4

\"103\" 0 79.3

\"104\" 0 87.5

\"105\" 0 83.5

\"106\" 0 78

\"107\" 0 78

\"108\" 0 85

\"109\" 0 84.7

\"110\" 0 92

\"111\" 0 72.3

\"112\" 0 83

\"113\" 0 96.9

\"114\" 0 85.7

\"115\" 0 85.4

\"116\" 0 85.3

\"117\" 0 93.5

\"118\" 0 86.8

\"119\" 0 87.9

\"120\" 0 87.2

\"121\" 0 53.8

\"122\" 0 89.8

\"123\" 0 91.1

\"124\" 0 88.6

\"125\" 0 92.3

\"126\" 0 97

\"127\" 0 89.5

\"128\" 0 88.2

\"129\" 0 92.2

\"130\" 0 78.9

\"131\" 0 90.3

\"132\" 0 87

\"133\" 0 113.7

\"134\" 0 98

\"135\" 0 100.2

\"136\" 0 79.4

\"137\" 0 90.3

\"138\" 0 77.7

\"139\" 0 83.9

\"140\" 0 75.5

\"141\" 0 60.6

\"142\" 0 71

\"143\" 0 71.8

\"144\" 0 76.8

\"145\" 0 102.7

\"146\" 0 94.25

\"147\" 0 79

\"148\" 0 66.6

\"149\" 0 71.8

\"150\" 0 74.8

\"151\" 0 68.2

\"152\" 0 62.3

\"153\" 0 61

\"154\" 0 77.5

\"155\" 0 57.4

\"156\" 0 71.4

\"157\" 0 70.3

\"158\" 0 80.2

\"159\" 0 84.2

\"160\" 0 111.3

\"161\" 0 80.7

\"162\" 0 97.9

\"163\" 0 123.2

\"164\" 0 72.9

\"165\" 0 83

\"166\" 0 75.9

\"167\" 0 70.7

\"168\" 0 67.1

\"169\" 0 69.2

\"170\" 0 67.05

\"171\" 0 70.5

\"172\" 0 70.8

\"173\" 0 71

\"174\" 0 69.1

\"175\" 0 62.9

\"176\" 0 94.8

\"177\" 0 94.6

\"178\" 0 108.2

\"179\" 0 97.9

\"180\" 0 75.2

\"181\" 0 74.8

\"182\" 0 94.2

\"183\" 0 76.1

\"184\" 0 94.7

\"185\" 0 86.2

\"186\" 0 79.6

\"187\" 0 85.3

\"188\" 0 74.4

\"189\" 0 93.5

\"190\" 0 87.6

\"191\" 0 85.4

\"192\" 0 101

\"193\" 0 74.9

\"194\" 0 87.3

\"195\" 0 90

\"196\" 0 94.7

\"197\" 0 76.3

\"198\" 0 93.2

\"199\" 0 80

\"200\" 0 73.8

\"201\" 0 71.1

\"202\" 0 76.7

3. Data on 102 male and 100 female athletes were collected at Institute of Sport. A subset of this dataset is available at \"ais_Wt.txt\", where we have the weight for each athlete (variable wt), Sex=0 means the athlete is male and Sex=1 means the athlete is female. the Australian a) Do we have paired observations? Why? b) Find the 95for the difference of weight between male and female.

Solution

a)

No, we don\'t have paired data as the data are collected from the set of two different groups. The one is female group and the other is male group. So, they are independent of each other. And hence the two sample data are collected independently and are unpaired.

b)

The 95% confidence interval can be calculated in R as -

First Import the data in R using the import button. My data file name is \'ais\'. So, I have used \'ais\'. if you have any other name, edit it.
> L = ais$Sex == \"1\"
> M = ais$Sex == \"2\"
> F_wt = ais[L,]$Wt
> M_wt = ais[M,]$Wt
> t.test(M_wt,F_wt)

   Welch Two Sample t-test

data: M_wt and F_wt
t = 9.2381, df = 197.71, p-value < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
11.94038 18.42168
sample estimates:
mean of x mean of y
82.52353 67.34250