Question

Question: Consider a normal distribution with mean m and

variance s2. Assume we know that s2 = 4 and suspect that m 6= 3. Assume further

that we have independently drawn 100 values from the distribution and have

obtained a sample mean of 5.

(a) Explain the notion of a sampling distribution and state the central limit

theorem.

(b) Approximately, what is the sampling distribution in the above situation?

Assume now that we want to conduct a hypothesis test concerning our suspicion

that m 6= 3.

(c) What are appropriate null and alternative hypotheses in this situation? Is the

test one-tailed or two-tailed?

(d) Explain the notion of a p-value.

(e) What is the p-value in the above situation? State which test statistic you are

using and why this is appropriate.

(f) For a significance level of a = 0:05, which conclusion can be drawn from

the test? Explain your reasoning.

(g) Explain the notion of a type 1 error. What is the probability of a type 1 error

in the above test?

This question uploaded just for study, not for examination help.. Kindly answer

Answer 1

(a)

Here we have

Sample size: n=100

The sampling distribution of sample mean will be approximately normal distribution with mean

and standard deviation is

(b)

Since sample size is large so sampling distribution of sample mean will be approximately normal distribution.

(c-g)

The type I error is denoted by . It is 0 in this case.