Module Five examined point estimates and confidence interval estimates. Module Six explores hypotheses and the process of hypothesis testing.
A hypothesis is a statement or claim about a population parameter developed for the purpose of testing. Some examples of hypotheses we may want to test include the following:
In many instances, it is too costly and time consuming to study every item in a large population to verify a claim made or a statement about a population parameter. A sample is typically taken from the population and tested to determine whether sufficient evidence exists to support or refute the statement about the population.
Lind, Marchal, and Wathen (2015) define hypothesis testing as “a procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement” and describe a six-step procedure used to develop a hypothesis test:
Step 1: State null and alternate hypotheses.
Step 2: Select a level of significance.
Step 3: Identify the test statistic.
Step 4: Formulate a decision rule.
Step 5: Take a sample; arrive at decision.
Step 6: Interpret the results.
In hypothesis testing, hypotheses are stated in pairs. The claim or statement made about a population parameter is placed in the alternative hypothesis HA (also referred to as the research hypothesis). The opposite of the statement in HA is used to populate the null hypothesis H0. H0 is a tentative assumption about the population parameter. Only H0can be tested directly. If the evidence from the sample is strong enough to reject H0, then HA is supported by default. If the sample evidence is not strong enough to reject H0, then H0 is not rejected but supported by the data. Note that only H0 can be tested directly. HA is tested by default.
For example, if the statement is the mean (µ) number of miles driven on a run-flat tire is less than 40,000 miles, then:
H0: µ ≥ 40,000
HA: µ < 40,000
The claim made in the problem (less than 40,000 miles) determines the sign in HA and the opposite of that sign is placed in H0. If the statement now is the mean number of miles driven on a run-flat tire is different from 50,000 miles, then:
H0: µ = 50,000
HA: µ ≠ 50,000
The claim made in the problem (different from 50,000 miles) determines the sign in HA and the opposite of that sign is placed in H0.
There are two generally accepted methods for testing hypotheses: the critical value method (also known as the rejection region method) and the p value method. The p value method, frequently used in research publications, is the method discussed in detail in Module Six. Note that the decisions reached by either method must be consistent. If H0 is rejected using the critical value method, it must also be rejected using the p value method.
Data set 2 presents a sample of the number of defective flash drives produced by a small manufacturing company over the last 30 weeks. The company's operations manager believes that the number of defects produced by the process is less than seven defective flash drives per week. Use this online calculator (or any statistical package that you are comfortable with) to construct a hypothesis test to verify the operations manager's claim. Your hypothesis test should include null and alternative hypotheses, a t test statistic value, a p value, a decision, and a conclusion. Submit a Word file that includes the hypothesis test.
For additional details, please refer to the Data Set Homework Guidelines and Rubric document
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