Long term experience showed that after a type of eye surgery it took a mean of 5.3 days recovery time in a hospital. However, a random sample of 32 patients with this type of eye surgery, were recently treated as outpatients during the recovery. The sample mean recovery time was 4.2 days. Does this indicate that the mean recovery time for all outpatients is less than the time for those recovering in the hospital? Use a = 0.01level of significance. Assume = 1.9 days. a. What is the level of significance? State the null and alternative hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? b. Identify the sampling distribution you will use. Explain the rationale for your choice. c. What is the value of the sample test statistic? Find the critical value(s). Draw a distribution that depicts the critical region. d. Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value. e. Based on your answers for parts a to d, will you reject or fail to reject the null hypothesis? State your conclusion in the context of the