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Hypotheses
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It covers all types of hypotheses in depth and it will be useful for exam recaps
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Seven steps of hypothesis testingLet us perform hypothesis testing through the following 7 steps of the procedure:
Step 1 : Specify the null hypothesis and the alternative hypothesis
Step 2 : What level of significance?
Step 3 : Which test and test statistic to be performed?
Step 4 : State the decision rule
Step 5 : Use the sample data to calculate the test statistic
Step 6 : Use the test statistic result to make a decision
Step 7 : Interpret the decision in the context of the original question
To guide us through the steps, let us use the following example.
Assume a food laboratory analyzed a certified reference freeze-dried food material with
a stated sodium (Na) content of 250 mg/kg. It carried out 7 repeated analyses and
obtained a mean value of 274 mg/kg of sodium with a sample standard deviation of 21
mg/kg. Now we want to know if the mean value of 274 mg/kg is significantly larger than
the stated amount of 250 mg/kg. If so, we will conclude that the reported results of this
batch of analysis were of bias and had consistently given higher values than expected.
Step 1 : Specify the null hypothesis and the alternative hypothesis
The null hypothesis Ho is the statement that we are interested in testing. In this case,
the null condition is that the mean value is 250 mg/kg of sodium.
The alternative hypothesis H1 is the statement that we accept if our sample outcome
leads us to reject the null hypothesis. In our case, the alternative hypothesis is that the
mean value is not equal to 250 mg/kg of sodium. In other words, it can be significantly
larger or smaller than the value of 250 mg/kg.
So, our formal statement of the hypotheses for this example is as follows:
Ho : 𝑥̅ = 250 mg/kg (i.e., the certified value)
H1 : 𝑥̅ ≠ 250 mg/kg (i.e., indicating that the laboratory has a bias result)
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