Hypothesis Testing: Continuous Variables

Question 1

How to start a hypothesis test for a continuous variable.

Answer 1

H0: μ=μ0 (This is the actual mean)
H1: μ < μ0 OR μ > μ0 OR μ≠μ0

Question 2

What is the second thing to do on the test

Answer 2

Write the distribution: Ẍn~N(μ0, sample variance/n)

Question 3

How to split the rejection regions

Answer 3

If you’re testing μ < μ0 then it is a negative value.
If you’re testing μ > μ0 then it’s a positive value.
If you’re testing μ ≠ μ0 then it is split in half, one at each side.

Question 4

How to find the rejection region in terms of c

Answer 4

Find the critical value in terms of Z.
Substitute all values into:
Z = c - μ / √variance/n.
When rearrganged you should be left with c. This is the rejection region and Ẍ is less than or greater than c.
Next, check x̄ to see if it is in the rejection region or not.

Question 5

How to find the rejection region using x̄

Answer 5

Find the critical value in terms of Z.
Then approxomate using:
z = x̄ - μ / √variance/n.
Check to see if this value of z is not in the rejection region Z.

Question 6

Instructions for carrying out a hypothesis test

Answer 6

1. Define the null and alternative hypotheses.
2. State significance level.
3. Determine the critical values.
4. Calculate the test statistic.
5. Decide whether it is in rejection region.
6. State the conclusion in words.