Assignment - HW Week 2 - 2.29 (a, b, c, e)

Given Data of photoresist thickness

T95 <- c(11.176, 7.089, 8.097, 11.739, 11.291, 10.759, 6.467, 8.315)
T100 <- c(5.263, 6.748, 7.461, 7.015, 8.133, 7.418, 3.772, 8.963)
PT <- cbind(T95, T100)
PT <- as.data.frame(PT)
print(PT)

##      T95  T100
## 1 11.176 5.263
## 2  7.089 6.748
## 3  8.097 7.461
## 4 11.739 7.015
## 5 11.291 8.133
## 6 10.759 7.418
## 7  6.467 3.772
## 8  8.315 8.963

Ans (a) Using two sample t-Test to check the claim of lower mean:

t.test(T95, T100, var.equal=TRUE, alternative="greater")

## 
##  Two Sample t-test
## 
## data:  T95 and T100
## t = 2.6751, df = 14, p-value = 0.009059
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
##  0.8608158       Inf
## sample estimates:
## mean of x mean of y 
##  9.366625  6.846625

Null hypothesis: Ho : u1=u2 : u1-u2=0

Alternative hypothesis: Ha : u1/=u2 : u1-u2 /= 0

The P-Value is 0.009059 which is less than 0.05. Therefore, we reject the null hypothesis Ho, and conclude that there is a lower mean photoresist thickness in wafers at higher baking temperature.

Ans (b)

The P-value for the test conducted is = 0.009059

Ans (c)

The 95 percent confidence interval is 0.8608158 <= u1-u2 <= infinity. The lower limit is greater than 0, which shows that there is a difference in the temperatures on the wafer thickness.

Ans (e) Checking the assumption of normality

qqnorm(PT$T95, main = "Normal Probability Plot for Thickness at 95 C")
qqline(PT$T95)

qqnorm(PT$T100, main = "Normal Probability Plot for Thickness at 100 C")
qqline(PT$T100)

As data points on both the probability distribution plots are mostly falling on a straight line, we can conclude that they appear to be normally distributed.

Source Code

# All R code used in document

T95 <- c(11.176, 7.089, 8.097, 11.739, 11.291, 10.759, 6.467, 8.315)
T100 <- c(5.263, 6.748, 7.461, 7.015, 8.133, 7.418, 3.772, 8.963)
PT <- cbind(T95, T100)
PT <- as.data.frame(PT)
print(PT)

library(dplyr)
t.test(T95, T100, var.equal=TRUE, alternative="greater")

qqnorm(PT$T95, main = "Normal Probability Plot for Thickness at 95 C")
qqline(PT$T95)
qqnorm(PT$T100, main = "Normal Probability Plot for Thickness at 100 C")
qqline(PT$T100)