Question 5.9

A Mechanical engineer is studying the thrust force developed by a drill press. He suspects that the drilling speed and the feed rate of the material are the most important factors. He selects four feed rates and uses a high and low drill speed chosen to represent the extreme operating conditions. He obtains the following results. Analyze the data and draw conclusions. Use Alpha 0.05.

observation<-c(2.7,2.78,2.83,2.86,2.45,2.49,2.85,2.8,2.6,2.72,2.86,2.87,2.75,2.86,2.94,2.88)
feed_rate<-c(rep(0.015,4),rep(0.030,4),rep(0.045,4),rep(0.060,4))
drill_speed<-c(125,125,200,200,125,125,200,200,125,125,200,200,125,125,200,200)
dat<-data.frame(feed_rate,drill_speed,observation)
dat$feed_rate <- as.factor(dat$feed_rate)
dat$drill_speed <- as.factor(dat$drill_speed)
Test_1 <- aov(observation~feed_rate*drill_speed,data = dat)
summary(Test_1)
##                       Df  Sum Sq Mean Sq F value   Pr(>F)    
## feed_rate              3 0.09250 0.03083  11.859  0.00258 ** 
## drill_speed            1 0.14822 0.14822  57.010 6.61e-05 ***
## feed_rate:drill_speed  3 0.04187 0.01396   5.369  0.02557 *  
## Residuals              8 0.02080 0.00260                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The p-Value is less than level of signifance therefore we reject Null hypothesis. There is enough data to conclude that Feed rate and Drill speed is Significant.