Now you will conduct another simulation study drawing samples from two

different normal distribution. Using rnorm() function, generate one random sample

data (with sample size n " 5) from the distribution Np3, 1q, and assign this data to an

object called sample3. Then generate another random sample data (with sample size

n " 5) from the distribution Np2, 1q, and assign this data to an object called sample4.

(a) Write down the five scores in sample3 and the five scores in sample4. Attach the

R code for generating the sample data.

(b) What are the mean score for sample3 and the mean score for for sample4? What

is the difference between these two means?

(c) What is the population mean difference between the two groups of scores? Is it

different from question 6 part (c)? Why?

Use t.test() function to conduct an independent two-sample t-test. Our null

hypothesis is H0 : 3 4 " 0. Our alternative hypothesis is Ha : 3 4 0.

The code is provided below. What are your obtained p-value and 95% confidence

interval? Suppose " 0.05. Is your test significant?

t.test(sample3, sample4, var.equal = T

(f) I will eventually tally the results across all students and compute the proportion

of students who got significant t-test after all assignments are submitted. Discuss

on the eClass discussion board whether this proportion represents type I error rate

(i.e., ) or power and explain why you pick your answer.