AppliedStatsLab8

# Lab Class 08 (17-05-2022)
# S Vijay Balaji (19BCE7571)

x1bar <- 74
n1 <- 40
sigma1 <- 8
x2bar <- 78
n2 <- 50
sigma2 <- 7
level <- 0.05
# calculation of z
z <- (x1bar - x2bar) / sqrt(((sigma1)^2 / n1) + ((sigma2)^2 / n2))
print(z)
pvalue <- 2 * pnorm(z, lower.tail = TRUE)
print(pvalue)
if (pvalue <= level) {
    print("Null Hypothesis H0 is rejected")
} else {
    print("Null Hypothesis H0 is accepted")
}

# Example 2: The research investigator is interested in studying wheather there is a significant difference
# in the salaries of B.Tech grades in two metropolian cities.
# A random sample of size 100 from kolkata yields an average income of Rs. 20,150. Another random sample of 60 from Delhi results in an average income of
# Rs. 20,250. If the variance of both the populations are given as sigma square = Rs. 40,000 and sigma square 2 = Rs 32,400 respectively,
# What is your conclusion?

x1bar <- 20150
n1 <- 100
sigma1 <- 40000
x2bar <- 20250
n2 <- 60
sigma2 <- 32400
level <- 0.05
# calculation of z
z <- (x1bar - x2bar) / sqrt(((sigma1)^2 / n1) + ((sigma2)^2 / n2))
print(z)
pvalue <- 2 * pnorm(z, lower.tail = TRUE)
print(pvalue)
if (pvalue <= level) {
    print("Null Hypothesis H0 is rejected")
} else {
    print("Null Hypothesis H0 is accepted")
}

# Example 3: A manufacturer claims that the average tensile strength of thread A exceeds the average tensile strength of thread B by at least 12 kgs.
# To test this claim, 50 pieces of each type of thread were tested under similar conditions. Type A thread had an average tensile strength of 86.7 kgs with a
# Standard devaiation of 6.28 kgs, while type B thread had an average tensile strength of 77.8 kilograms with a standard devation of 5.61 kgs.
# Test the manufacturer's claim using a 0.05 level of significance.

x1bar <- 86.7
n1 <- 50
sigma1 <- 6.28
x2bar <- 77.8
n2 <- 50
sigma2 <- 5.61
level <- 0.05
# calculation of z
z <- (x1bar - x2bar) / sqrt(((sigma1)^2 / n1) + ((sigma2)^2 / n2))
print(z)
pvalue <- 2 * pnorm(z, lower.tail = TRUE)
print(pvalue)
if (pvalue <= level) {
    print("Null Hypothesis H0 is rejected")
} else {
    print("Null Hypothesis H0 is accepted")
}