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.

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

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