8 steps of hypothesis testing

Inferential Statistics and Analytics
Deliverable #4
Jeff Rover
Rasmussen College
12/09/17
Deliverable 04 Worksheet
1. Describe the 8 steps in the process for hypothesis testing. Explain the decision criteria for rejecting the null hypothesis for both the p-value method and the critical value method.

Answer and Explanation:

8 Steps to test hypothesis

1) Explain the questions (asked) in words

2) Determine the null and alternative Hypothesis

3) Find out the signifience level

4) Find the rejection and acceptance region

5) Create bell curve and find the critical values

6) Find the test statistics

7) Conclude the result (accept or reject Ho)

8) Conclude the result in words

The remaining problems refer to the following scenario:

A claim is made that the average salary for all jobs in Minnesota is less than $65,000. You are going to test the claim using and assume that your data is normally distributed and the population standard deviation is not known.

2. Write the null and alternative hypotheses symbolically and identify which hypothesis is the claim. Then identify if the test is left-tailed, right-tailed, or two-tailed and explain why.

Answer and Explanation:

Let µ represent the average salary for all job in Minnesota: the claim is Cleary mentioned

µ<$65000 hence our hypothesis can be written this:

Null Hypothesis Ho: µ=$65000

Alternative Hypothesis Ho: µ<65000

From the claim (µ<65000) we can easily conclude that test is left tailed test.

3. Identify and explain which test statistic you will use for your hypothesis test: z or t? Find the value of the test statistic.

Answer and Explanation:

The sample size is large n=364 so we will use Z-test:

And formula for Z-test is:

Mean= 62306.12637

Standard Deviation=19149.21386

Count (n) =364

Z

Z=

(Excel sheet is for calculation)

4. What is the critical value? Describe the rejection region.

Answer and Explanation:

Critical values: The values of the test statistic that separate the rejection and non-rejection regions.

If Z is less than or greater than critical value reject the null hypothesis otherwise accept:

For α=0.05 the critical values are

In our case this the left tailed test so will use Z<-1.96 as rejection of Ho

5. Using the critical value approach, should you reject the null hypothesis or not reject the null hypothesis? Explain. After making your decision, restate it in non-technical terms and make a conclusion about the original claim.

Answer and Explanation:

Our data Z score is Z= -2.683965697

Critical value Z= -1.96

-2.683965697 < -1.96 so reject the null hypothesis and there is sufficient evidence to support the claim and conclude that the average salary is less than $65000

6. Calculate the p-value for this hypothesis test, and state the hypothesis conclusion based on the p-value. Does this match your results from the critical value method?

Answer and Explanation:

Alpha = a = 0.05

P values of the left tailed Z score (Z= -2.683965697) = 0.003637729

So P-value < alpha (0.003637729<0.05) reject the null hypothesis at a=0.05 and there is sufficient evidence to support the claim and conclude that the average salary is less than $65000