Problem No. 2.29

knitr::opts_chunk$set(echo=TRUE)

##As per given data in the problem regarding the photoresist thickness in (kA) for eight wafers baked at 95°C and 100°C temperatures,

p95<-c(11.176,7.089,8.097,11.739,11.291,10.759,6.467,8.315)
q100<-c(5.263,6.748,7.461,7.015,8.133,7.418,3.772,8.963)

To calculate Mean and Median,

summary(p95)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   6.467   7.845   9.537   9.367  11.205  11.739

##The summary description of p95 data shows the minimum or lowest photoresist thickness at 95°C is 6.467 kA and maximum is 11.739 kA with a mean 9.367 kA. The first quartile is 7.845 kA While the third quartile is 11.205 kA.

summary(q100)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   3.772   6.377   7.216   6.847   7.629   8.963

##The summary description of q100 data shows the minimum or lowest photoresist thickness at 95°C is 3.772 kA and maximum is 8.963 kA with a mean 6.847 kA. The first quartile is 6.377 kA While the third quartile is 7.629 kA.

Testing Hypothesis,

##*The null hypothesis here is that 95°C column and 100°C column have an equal mean.

##mean95°C=mean100°C

##*The alternative hypothesis is that the mean of 95°C column is greater than the 100°C column.

##*mean95°C Column>100°C column

Now performing t-test,

t.test(log(p95),log(q100),var.equal=TRUE, alternative = 'greater')
## 
##  Two Sample t-test
## 
## data:  log(p95) and log(q100)
## t = 2.5046, df = 14, p-value = 0.01262
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
##  0.09507682        Inf
## sample estimates:
## mean of x mean of y 
##  2.213906  1.893530

The p value for the two sample t-test is 0.01262

The 95% confidence interval is 0.0950 to Infinity

As the p value is less than the 0.05,hence we reject the null hypothesis.

Conclusion:- From the p value, null hypothesis is rejected and we conclude that the higher temperature results in wafers with a lower mean photoresist thickness.

Now plotting Normal Probability Plots

qqnorm(p95,main= "Normal Probability plot for 95°Celcius", ylab= "Thickness of photoresist")
qqline(p95)

##From the Normal distribution probability plot of 95°C we can state that the data is normally distributed and 75% of the photoresist thickness data is within 2 standard deviation from the mean.

qqnorm(q100,main= "Normal Probability plot for 100°Celcius",ylab= "Thickness of photoresist")
qqline(q100)

##From the Normal distribution probability plot of 100°C we can state that the data is normally distributed and 75% of the photoresist thickness data is within 2 standard deviation from the mean.