Question

Kindly answer the following question by using Rstudio.

At Mayo Clinic evaluated the link between obesity and energy spent on daily activities by attaching sensors to two groups (Slim and Overweight) and monitored energy spent on different activities (stand/walk, sit, lie).

A.1 Plot the data using a dotplot and comment on anything you notice relative to the analysis for the sitting variable.

A.2 For sitting, test the hypothesis that there is no difference between the slim and Overweight groups. Summspecifyingspecifing null and alternative hypotheses, test statistic, degrees of freedom, p-value and conclusion.

Group

Subject

Stand/walk

Sit

Lie

Overweight	11	260.244	646.281	521.044
Overweight	12	464.756	456.644	514.931
Overweight	13	367.138	578.662	563.3
Overweight	14	413.667	463.333	532.208
Overweight	15	347.375	567.556	504.931
Overweight	16	416.531	567.556	448.856
Overweight	17	358.650	621.262	460.55
Overweight	18	267.344	646.181	509.981
Overweight	19	410.631	572.769	448.706
Overweight	20	426.356	591.369	412.919

slim	1	511.100	370.300	555.5
slim	2	607.925	374.512	450.65
slim	3	319.212	582.138	537.362
slim	4	584.644	357.144	489.269
slim	5	578.869	348.994	514.081
slim	6	543.388	385.312	506.5
slim	7	677.188	268.188	467.7
slim	8	555.656	322.219	567.006
slim	9	374.831	537.031	531.431
slim	10	504.700	528.838	396.962

Answer 1

A1. I created two variables as "sitting.ow" for sitting column for overweight group and "sitting.slim" for slim group

I combined both variables as another variable "x" and run the dotchart function to get the plot of the data

the R code is as follows,

sitting.ow=c(646.281,456.644,578.662,463.333,567.556,567.556,621.262,646.181,572.769,591.369)
sitting.slim=c(370.300,374.152,582.138,357.144,348.994,385.312,268.188,322.219,537.031,528.838)
x=c(sitting.ow,sitting.slim)
dotchart(x)

the output is given by,

300 400 500 600

from the above plot we can observe that the values of group slim, 7 out of 10 are scattered below 400 and the values of group overweight , 9 out of 10 are scattered above 500.

from this we can say that the group "overweight" spent more energy than the group "slim".

A2.

the null hypothesis will be,

H0: there is no significant difference between the two groups.

H1: there is a significant difference between two groups.

The test statistic of t-test for two independent samples is given by,

t=(x1- x2)/ : where x1 and x2 are the means of the two variables,

n1 and n2 are sizes of x1 and x2 respectively

and   are the standard deviations of x1 and x2 respectively

the test statistic follows t distribution with (n1+n2 - 2) degrees of freedom.

the R code and the result of the test is given as follows ,

> t.test(sitting.ow,sitting.slim,paired=FALSE)

   Welch Two Sample t-test

data: sitting.ow and sitting.slim
t = 4.202, df = 15.203, p-value = 0.000749
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
80.77473 246.68467
sample estimates:
mean of x mean of y
571.1613 407.4316

CONCLUSION: since the p-value (0.000749) is less than 0.05 , we may reject the null hypothesis and conclude that there is a significant difference between the means of the two groups (i.e., overweight and slim)