A Bureau of Labor Statistics (BLS) economist conducts a statistical study to tes

Question

A Bureau of Labor Statistics (BLS) economist conducts a statistical study to test his hunch that in households with a minimum-wage worker, mean household debt changes following a hike in the minimum wage. Suppose the mean household debt stays the same following a minimum-wage hike. However, when the economist collects a random sample, the sample mean difference is actually greater than zero.

Does this mean the economist made a mistake in his research? Explain why/why not.

Suppose the economist collects a random sample and decides to conduct a hypothesis test. Formulate the null and alternative hypothesis:

Explanation / Answer

Ans) If there is a hike in the wage then household debts in the households with a minimum wage worker may increase or decrease or remain same. With the hike of minimum wage not all households with a minimum wage worker will tend to spend more or spend less. In some households household debt may increase due to increase in spending which is more than income, in some other households household debt may decrease due to less spending than income and in some other household it remains same as before the increase in minimum wage. But given mean household debt remains same following minimum wage hike. It is due to decrease in household debt in some household nullifies the increase in household debt in some other households. But when we collect sample and observe the mean it may be that the difference will greater than zero as we are not covering all the households. Suppose we collects households which have all increase in household debts. Then minimum wage increase will indicate increase in household debt but which not actually for whole population. So this does not mean economist made a mistake.

The null hypothesis states the exact opposite of what an researcher expects. Here the researcher believes that household debts changes due to hike in minimum wage.So its exact opposite is the null hypothesis. To conduct a hypothesis test in this regard the null hypothesis will be "in the households with minimum wage workers, mean household debt remains same with a hike in the minimum wage" and the alternative hypothesis will be " in the households with minimum wage workers, mean household debt will increase or decrease with a hike in the minimum wage." The null hypothesis states the exact opposite of what an researcher expects. Here the researcher believes that household debts changes due to hike in minimum wage.So its exact opposite is the null hypothesis.

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