A health insurer wants to know if having a nurse available to answer simple questions over a telephone hotline could cut the costs of unnecessary doctor visits. Records show the average cost per family is typically around $900 with an SD of $1,000 and the cost distribution is skewed with a tail to the right. They decide to conduct an experiment in which they randomly select 2,500 families, give them access to the hotline and record their health-care costs. After doing this, in the sample of families with hotline access they observe that the average cost per family is $850. Is there evidence here that the hotline actually reduces costs?

a) Justify your answer with a test of statistical significance

b) Compute and give a brief interpretation of the corresponding p-value in this setting.

c) Should the fact that the cost distributions were skewed affect the calculations you made in part (b)? Explain.