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:
In hypothesis testing, the first step is to identify the claim to be tested. Step number two is to give the symbolic form that must be true when the original claim is false. This step is when you establish your alternative hypothesis and can determine if it is true or not. Step 3 is to identify the Null and Alternative Hypothesis. These are identified by using Ho for the null hypothesis and H1 or Hafor the alternative hypothesis. Step 4 is selecting the significance level. The significance level is represented by α (alpha) during hypothesis testing. This is also known as the confidence level. Step 5 is identifying the test statistic. There are two different test statistics’, z-score and t-statistic. The Z-score (z) is used when sigma, population standard deviation (σ) is known (this is uncommon). The t-statistic () will be used when the standard deviation (σ) sigma is not known. Next is step number six, in this step, you will determine if you should reject the null hypothesis or not. In determining if the null hypothesis should be rejected or not you can use either the p-value method or the critical value method. The p-value method you are finding the probability of the test statistic whereas the critical value method is determiningwhere the rejection region begins and then compares the test statistic to that number. There are two types of test, one-tailed and two-tailed. Step number seven is where you decide to either reject the null hypothesis or not. If you used the p-value, you would reject (Ho) if the p-value is less than or equal to the significance level (p-value ≤ α) or you will fail to reject Ho if the p-value is greater than the significance level (p-value > α). You should get the same result with both methods. The final step in hypothesis testing is to come to a conclusion and restate the decision in nontechnical terms by noting that there is either sufficient evidence to support or to reject the claim in your test.
The remaining problems refer to the following scenario:
A claim is made that the average salary for all jobs in Minnesota is less than $75,000. 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:
The claim in this scenario is saying that the average salary for all jobs in Minnesota is less than $75,000.
Symbolically the null hypothesis will be written as: Ho: μ = $75,000 and the alternative hypothesis will be written as Ha: μ < $75,000.
This test is left-tailed as we are testing that the average salary is less than $75,000. Since this is a left-tailed test, the rejection region will be left of the critical value under the curve.
A claim is made that the average salary for all jobs in Minnesota is less than $75,000. You are going to test the claim using and assume that your data is normally distributed and the population standard deviation is not known.
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:
Since our population standard deviation is unknown, I will use the t-test statistic. The formula for t-test statistic is: = (x̅ – μ) / (s /). With the previous data I collected, I know the sample mean, sample standard deviation and the sample size: x̅ = 71,879 s = 23367.36 and = 364. The population mean we are using in this scenario is μ = 75,000.
So, with that information I can calculate the t test statistic in excel:
= (71879 – 75,000) / (23367.36 / sqrt (364))
which gives me an answer of = -2.548.
4. What is the critical value? Describe the rejection region.
Answer and Explanation:
Now I need to determine the critical value. Since this is a left tailed test, the formula to find the critical value usingexcel is =T.INV (α, df).
The significance level for this scenario is α =.05
Our degrees of freedom (df)= 363. The degrees of freedom were determined by taking the sample size of 364 and subtract 1.
The formula would be entered as = T.INV (0.05, 363) The answer I get is -1.649 My critical value = -1.649.
-2.548 > -1.649
Since our test statistic is greater than our critical value the rejection region is to the left of our critical value of -1.649 and includes our test statistic
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:
To determine if I should reject or not reject the null hypothesis, I will need to compare my test statistic and my critical value. My test statistic is = -2.584 and my CV = -1.649.
This would be: -2.548 < -1.649
This means that the test statistic falls in the critical region also known as the rejection region and the null hypothesis should be rejected.
Since I reject the null hypothesis, it means that the average salary for all jobs in Minnesota does not equal $75,000. This proves my alternative hypothesis to be true, meaning that the average salary for all jobs in Minnesota will be less than $75,000.
To restate it in non -technical terms and make a conclusion on the original claim would be written as: There is sufficient evidence to support the claim that the average salary for all jobs in Minnesota is less than $75,000.
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:
I will now calculate the p-value for the same hypothesis test.
To calculate the p-value, the excel formula will be =T.DIST (t,df,true). We already have our values needed for this formula.
= -2.548 and df= 363. So in excel I entered =T.DIST(-2.548, 363, true) and got my p-value of 0.0056.
When using the p-value to decide whether to reject the null hypothesis or not, I will need to compare it to the significance level. For this scenario the significance levelor α = .05.
The comparison would read 0.05 <.0056
Based on the comparison, I know that I must reject the null hypothesis since the p-value would fall within the critical region (Rejection region).
My conclusion would be: There is sufficient evidence to support the claim that the average salary for all jobs in Minnesota is less than $75,000.
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