The actual test begins by considering two hypotheses. They are called the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints. \(H_0\): The null hypothesis: It is a statement of no difference between the variables—they are not related. This can often be considered the status quo and as a result if you cannot accept the null it requires some action. \(H_a\):
The alternative hypothesis: It is a claim about the population that is contradictory to \(H_0\) and what we conclude when we reject \(H_0\). This is usually what the researcher is trying to prove. Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data. After you have determined which hypothesis the sample supports, you
make a decision. There are two options for a decision. They are "reject \(H_0\)" if the sample information favors the alternative hypothesis or "do not reject \(H_0\)" or "decline to reject \(H_0\)" if the sample information is insufficient to reject the null hypothesis. \(H_{0}\) always has a symbol with an equal in it. \(H_{a}\) never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (including one of the co-authors in research work) use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis. Example \(\PageIndex{1}\) Exercise \(\PageIndex{1}\) A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses. Answer
Example \(\PageIndex{2}\) We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are:
Exercise \(\PageIndex{2}\) We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol \((=, \neq, \geq, <, \leq, >)\) for the null and alternative hypotheses.
Example \(\PageIndex{3}\) We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:
Exercise \(\PageIndex{3}\) We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.
Example \(\PageIndex{4}\) In an issue of U. S. News and World Report, an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.
Exercise \(\PageIndex{4}\) On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. Fill in the correct symbol (\(=, \neq, \geq, <, \leq, >\)) for the null and alternative hypotheses.
COLLABORATIVE EXERCISE Bring to class a newspaper, some news magazines, and some Internet articles . In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class. ReviewIn a hypothesis test, sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we:
Formula Review\(H_{0}\) and \(H_{a}\) are contradictory.
\(\alpha\) is preconceived. Its value is set before the hypothesis test starts. The \(p\)-value is calculated from the data.References Data from the National Institute of Mental Health. Available online at http://www.nimh.nih.gov/publicat/depression.cfm. GlossaryHypothesisa statement about the value of a population parameter, in case of two hypotheses, the statement assumed to be true is called the null hypothesis (notation \(H_{0}\)) and the contradictory statement is called the alternative hypothesis (notation \(H_{a}\)).What is an example of a null hypothesis and alternative hypothesis?Null Hypothesis: On the average, the dosage sold under this brand is 50 mg (population mean dosage = 50 mg). Alternative Hypothesis: On the average, the dosage sold under this brand is not 50 mg (population mean dosage ≠ 50 mg). This is a two-sided alternative hypothesis.
How do you solve for null and alternative hypothesis?The general procedure for null hypothesis testing is as follows:. State the null and alternative hypotheses.. Specify α and the sample size.. Select an appropriate statistical test.. Collect data (note that the previous steps should be done prior to collecting data). Compute the test statistic based on the sample data.. What are examples of null hypothesis?The null hypothesis assumes that any kind of difference between the chosen characteristics that you see in a set of data is due to chance. For example, if the expected earnings for the gambling game are truly equal to zero, then any difference between the average earnings in the data and zero is due to chance.
What is the null and alternative hypothesis for each research question?Basically, the difference between a null and alternative hypothesis is that the former contradicts the research question, while the latter affirms it. In short, a null hypothesis is a negative statement relative to the research question, and an alternative hypothesis is a positive statement.
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