An insurance company's researcher is interested in determining whether the costs of treating patients with back pain is significantly different for managed care patients versus those with traditional insurance coverage. On average, traditional insurance pays an average of $3,455 per patient for such cases. Under managed care, a sample 25 patients yielded an average cost of $3,155 with a standard deviation of $235.
1. Write the statement for the null and alternative hypothesis that managed care costs for back pain are significantly different from the cost of treating a patient under traditional insurance.
2. Perform a hypothesis test at the .05 level of significance testing whether or not the cost for the treatment of back pain is significantly different for managed care versus traditional insurance.
State your conclusion as to whether or not managed care costs for back pain are significantly different from those of traditional insurance.