Problem 1

A normal population distribution has a mean of 10 and an unknown standard deviation. We want to calculate the probability of obtaining a sample mean of 12 or greater if the sample standard deviation (s) is 2 and sample size (n) is 4. Answer the following questions.

a) Calculate the standard error of sample mean (SE means. = ). Explain what this number

b) Calculate t-score of the sample mean 12. Use t = SE

c) Use R command pt() to verify that P(X 2) is approximately 0.07. Copy and paste your R command and output.