Question

2. Samples of each of three types of stopwatches were tested. 21 watches of type I, 16 watches of tyep II and 11 watches of type III were randomly selected. The cycles (on-off-restart) survied until some part of the mechanism failed were measured. Below shows part of the R output from analyzing these data. Df --.754.4 Sum Sq Mean Sq F value type Residuals 56.7 (a) Complete the ANOVA table. (b) Write the formula for estimating σ2 (using our usual one-way ANOVA model notation), and compute the estimate from the table. (c) Calculate the total sum of squares (d) Test whether there is significant difference among the types. Conduct your test at the significance level a0.05

Answer 1

Ans:

a)N=21+16+148

df(type)=3-1=2

df(residual)=48-3=45

SS(residual)=45*56.7=2551.5

MS(type)=754.4/2=377.2

F=MS(type)/MS(residual)=377.2/56.7=6.65

Source	df	SS	MS	F
type	2	754.4	377.2	6.65
residuals	45	2551.5	56.7
total	47	3305.9

b)

$\sigma ^2$ =MS(residual)=56.7

c)SS(total)=754.4+2551.5=3305.9

d)F=6.65

p-value=FDIST(6.65,2,45)=0.0029

As,p-value<0.05,we reject the null hypothesis.

There is sufficient evidence to conclude that there is significant difference among the types.