TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Levajkovic)/Übungen 2023W/HW09.1

Two-sample t-test

Create two independent samples from the normal distribution. The first sample of size 10 shall be taken from the N(0,1)-distribution. The second sample of size 20 shall be taken from the N(−1,1) distribution. Test the null hypothesis that the populations means are equal with a (two-sided) two-sample t-test on the 5%-significance level:

• (a) Calculate the t-statistic (without t.test())
• (b) Compare it to the output of t.test()
• (c) Interpret the result of the test

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Lösungsvorschlag von Friday

--Friday Sa 30 Jan 2021 17:33:10 CET

# Statistics and Probability: HW #9
# Friday 
# Duedate: 07.12.2020

# Problem 1 - Two-sample t-test
# Create two independent samples from the normal distribution. The first sample 
# of size 10 shall be taken from the N(0,1)-distribution. The second sample of 
# size 20 shall be taken from the N(−1,1) distribution. Test the null hypothesis
# that the populations means are equal with a (two-sided) two-sample t-test on 
# the 5%-significance level:
n1 <- 10
data1 <- rnorm(n1, 0, 1)
md1 <- mean(data1)
sd1 <- sd(data1)

n2 <- 20
data2 <- rnorm(n2, -1, 1)
md2 <- mean(data2)
sd2 <- sd(data2)

alpha <- 0.05

# Problem 1a)
# Calculate the t-statistic (without t.test())
t <- (md1-md2)/sqrt((sd1^2)/n1 + (sd2^2)/n2)
t

# Problem 1b)
# Compare it to the output of t.test()
t.test(data1, data2)

# Problem 1c)
# Both previous calculate the same t value.
# Since the p-value > alpha we do not reject the null hypothesis