Step-by-Step Hypothesis Testing
There is a step-by-step process to help you test a hypothesis. The purpose of the hypothesis testing is to determine if the value claimed by the null can be rejected with the new research, or not.
Hypothesis testing can be conducted on many types of data (means, proportions, slope, etc.) The test is conducted on a sample to see if evidence of a difference exists to be applied to the population.
*Note: this guide may use symbols you aren’t familiar with. View our complete list of Statistics Symbols here.
Making hypothesis conclusions
Step 1: Determine the null and alternate hypothesis
Step 2: Find the test statistic
Step 3: Find the p-value or the critical value
Step 4: Draw conclusions based on the p-value (by comparing it to the significance level) or critical value (by seeing if the test statistic lies in the rejection region)
Types of Hypothesis Tests: Left, Right and Two-tailed tests
The type of test is determined by the sign on the alternate hypothesis. Depending on the sign we will be looking at certain regions in the normal curve to make our conclusion.
Now you Try! Practice Problems
Example One
One Sample Hypothesis Test using the P-value approach
A detergent manufacturing company conducted a survey in 2017 and found that 77% of its customers were satisfied with their product. In 2019, they conducted the survey again and found that out of 894 customers 652 customers were satisfied
- Is their evidence that their customers satisfaction rate has changed?
- Test this at alpha α=0.05 level of significance.
1. Determine the null and alternate hypothesis:
Since this problem involves proportions we have to find out the proportion of customers who were satisfied. Since 652 out of 894 were satisfied the sample proportion is p̂ = 652/894 = 0.729
- Null hypothesis: H0: p = 0.77
- Alternate hypothesis: H1: p ≠ 0.77
- Since the alternate has a ‘≠ ‘sign, this is a two tailed test.
2. Find the test statistic:
Given p0 = 0.77; p̂ =0.73; number of observations, n = 894
The test statistic can be found in the following way:
3. State the Conclusion
- The P-value is found to be 0.0038 (See the tech help section for further assistance)
-
Is the P-value less than the level of significance alpha,α?
- Yes
-
Is there evidence to reject the null in favor of supporting the alternate?
- Yes. The P-value has shown evidence of a significant change or difference.
- Therefore, there is evidence that the customer satisfaction has changed.
Tech Help
In StatCrunch
Step 1: Select → Stat, Proportion stats, One Sample, with Summary
Step 2: Enter the values as shown on the left
You will see the results on the right (here, they are shown below).
In the graph the p-value is the region to the left and right of |z| = 2.891. The area is shaded in red.
In Excel
Step 1: Plug in the formula for z statistic that was shown above
In this example, we will find the following result
From the Z-table
Look for -2.8 in the first column and go across the row to the last column which is 0.09. Adding - 2.8 and 0.09 we get -2.89. The value in the box intersecting -2.8 row and 0.09 column gives the p-value.
This is a one tailed value. Multiply this by 2 to get the 2 tailed value
In Python
For a two-tailed test, we can find the p-value for one tail and multiply it by two. Multiplying by 2, we get the p-value as 0.0038
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