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

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 her 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 decreases or stays the same following 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 is unaffected by a hike in the minimum wage. The economist commits a Type I error if she 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 actuary 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

Solution:-

The economist formulates the null hypothesis as

Null hypothesis:- In household with a minimum wage worker, mean household debt decreases or stay the same following a hike in the minimum wage.

Type I error if she concludes that

Mean Debt increases following a minimum wage hike when it actually does not.

p - value is 0.12 which is greater than significance level(0.05), hence the sample data does not provide sufficient evidence against the null hypothesis.

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