Q1. Obtain a normal probability plot of the sample and comment on what you see.

Given data set

data <- c(4.52, 1.02, 0.27, 10.38, 13.04, -4.10, 8.21, -0.64, 4.35, 2.74, 14.00, 16.05, 5.57, 19.23, 7.52, 7.01, -0.63, 2.78, 7.64, 0.10)

Generate the normal probability plot

qqnorm(data) qqline(data, col = “red”)

If the points in the Q-Q plot fall approximately along the reference line,

we can conclude that the data is approximately normally distributed. Deviations

from the line suggest departures from normality.

Q2. Implement a t-test in R for H0: µ = 5 vs Ha: µ > 5. Let α = 0.01.

Perform a one-sample t-test

t_test_result <- t.test(data, mu = 5, alternative = “greater”, conf.level = 0.99)

Print the result of the t-test

print(t_test_result)

Q3. Use R to calculate the 99% confidence interval for the population mean.

The t-test result already includes the confidence interval

ci <- t_test_result$conf.int

Print the 99% confidence interval

print(paste(“99% Confidence Interval:”, round(ci[1], 3), “to”, round(ci[2], 3)))