Question

This problem is to be done in R.

Maria claims that she has drawn a random sample of size 30 from an Exp(10) distribution (λ = 10, rate = 0.1). The mean of her sample is 12.

(a) What is the expected value of a sample mean?

(b) Run a simulation by drawing 1000 random samples, each of size 30, from an Exp(10) distribution, and compute the means for each sample. What proportion of the sample means are ≥ 12?

(c) Do you think a mean of 12 for Maria’s sample is unusual for a sample of size 30 from an Exp(10) distribution?

Answer 1

The sample mean 12 is may be occur but most of values of sample mean will be near around 10.

sample mean 12 is not unusual it may be occur in some cases.