Question

please solve with R and provide the codes too

A consulting firm is studying the effects of leadership structure on team performance. Four structures are considered, and seven teams are randomly assigned to each structure type. Results on a proprietary performance index are as follows: А 31.8 36.6 36.9 36.6 34.0 35.2 38.0 31.5 25.1 34.8 25.7 23.9 40.8 34.9 30.5 28.5 39.0 39.2 34.2 35.6 39.4 23.5 29.6 40.9 42.0 29.5 33.9 11. State your null and alternate hypotheses. 12. Do the different leadership structures have the same effect on team performance? 33.3

Answer 1

The R code is

A=c(36.9 ,35.2, 36.6, 40.8,39.0, 35.6, 40.9)
B=c(36.6, 38.0 ,34.8 ,34.9 ,39.2, 39.4, 42.0 )
C=c(31.8 ,31.5 ,25.7 ,30.5 ,33.3 ,23.5, 29.5)
D=c( 34.0,25.1, 23.9,28.5, 34.2, 29.6 ,33.9)
tr=c("A","B","C","D")
t=rep(tr,each=7)
x=c(A,B,C,D)
d=data.frame(x,t)
aov=aov(x~t,data=d)
summary (aov)

The Output is

>A=c(36.9 ,35.2, 36.6, 40.8,39.0, 35.6, 40.9)
>B=c(36.6, 38.0 ,34.8 ,34.9 ,39.2, 39.4, 42.0 )
>C=c(31.8 ,31.5 ,25.7 ,30.5 ,33.3 ,23.5, 29.5)
>D=c( 34.0,25.1, 23.9,28.5, 34.2, 29.6 ,33.9)
>tr=c("A","B","C","D")
>t=rep(tr,each=7)
>x=c(A,B,C,D)
>d=data.frame(x,t)
>aov=aov(x~t,data=d)
>summary (aov)

Df Sumsq Mean Sq Fvalue P(>F)

t 3 472.3 157.44 14.4 1.42e

Residuals 24 262.4 10.93

- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Answers

Here Pvalue=1.42e which is approximately zero

The p-value is = 0

since pvalue = 0 & alpha= 0.05

pvalue=0< alpha=0.05, it is concluded that the null hypothesis is rejected

12)

The Null and alternative hypotheses to be tested:

Ho: μ1 = μ2 = μ3 = μ4 i.e the different leadership structures have the same effect on team performance

Ha: Not all means are equal i.e. the different leadership structures have not same effect on team performance

13)

Here P value is less than level of significance alpha=0.05 then we reject the null hypothesis and conclude that  the different leadership structures have not same effect on team performance