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Developing the null and alternative hypotheses, Type I and II errors, interpreti

ID: 3231704 • Letter: D

Question

Developing the null and alternative hypotheses, Type I and II errors, interpreting p-values 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 increases (spending increases more than income) following a hike in the minimum wage. The economist formulates the null hypothesis as: In households with a minimum-wage worker, mean household debt decreases following a hike in the minimum wage. In households with a minimum-wage worker, mean household debt is unaffected by a hike in the minimum wage. In households with a minimum-wage worker, mean household debt increases following a hike in the minimum wage. In households with a minimum-wage worker, mean household debt decreases or stays the same following a hike in the minimum wage. The economist commits a Type I error if he concludes that: Mean debt increases following a minimum-wage hike when it actually does not. Mean debt does not increase following a minimum-wage hike when it actually does. Suppose that the economist conducts the hypothesis test and uses the value of the test statistic to compute a p-value for the test. The p-value is 0.12. Using the guidelines suggested by statisticians for interpreting small p-values, the sample data provide evidence against the null hypothesis.

Explanation / Answer

From the information, observe that a bureau of labour statistics economist conducts a statistical study to test his hunch that in households with a minimum-wage worker.

The null hypothesis as follows:

Answer: A

That is, in household with a minimum-wage worker, mean household debt decreases following a hike in the minimum wage.

The Type-II error as follows:

Answer: B

That is, minimum debt does not increase following a minimum-wage hike when it actually does.

Assume that the level of significance is 0.05

Here, the economist conducts a hypothesis test.

The p-value is 0.12

Therefore, the sample data provide a weak evidence against the Null hypothesis.

Since the p-value exceeds the level of significance.