Introduction to Statistics: Objectives
- Test of the null hypothesis using t-test and confidence intervals. Power assessment of the hypothesis test using Power analysis.
Hypothesis testing
Example 1 Filling cereal boxes
The purpose of this example is to introduce the concepts of hypothesis testing. You will use a one-sample t-test to analyze processed data to determine if the process is on target.
issue
The objective: You want to determine if the process is on target.
Data collection
To evaluate the process of the mean. You will choose 6 boxes of cereal at random, weigh them, and use the sample data to estimate the population mean.
Tools
Stat> Basic Statistics> 1-Sample t
Hypothesis testing
What is a hypothesis test?
A hypothesis test uses sample data to test a hypothesis about the population from which the example is taken. The one-sample t-test is one of many procedures available for hypothesis testing in MINITAB.
For example, suppose you want to test the piston wheel measurement equals the desired length of the target. You will measure a number of wheels and use the measurement of those example wheels to estimate the wheel size from the population. This is an example of a stastistical inference, using information about an example to make an inference about a population
When to use a hypothesis test?
Use a hypothesis test when you have sample data and you want to make inferences about one or more populations.
Why use a hypothesis test?
Hypothesis testing can help answer questions such as:
- Is the process correctly focused? Is the product of one supplier better than the product of another? Are there differences between the treatment of the groups and the experiments?
For example,
- Is your assortment of your paper on average 8.5 inches wide? Is supplier's gasoline of a higher octane rating than supplier B's? Does the customer prefer one formulation of one beverage over another?
Testing the null hypothesis
You need to determine if the mean of a packaging process differs significantly from the correct weight of 365 grams. In statistical terms, the mean process is also called the population mean.
Statistical hypothesis
There are 2 possibilities, µ is equal to 365 or it is not. These alternatives can be used as 2 hypotheses:
- The null hypothesis (H0): µ is equal to.365 grams The alternative hypothesis (H1): µ is not equal to 35 grams
Because you can't measure every box in the population, you can never know exactly which hypothesis is correct. However, a proper hypothesis test can help you make a formal calculation. For these data the appropriate test is the one-sample t-test.
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