Suppose we're testing a new antibacterial cream, "Formulation CS," on a small cut made on the inner forearm. We know from previous research that with no medication, the mean healing time (defined as the time for the scab to fall off) is 7.6 days, with a standard deviation of 1.4 days. The claim we want to test here is that Formulation CS speeds healing. Use a 5% significance level. Our procedure is that we cut 25 volunteer college students and apply Formulation NS to the wound. The mean healing time for these subjects is days. We will assume that the standard deviation is days. So, with a significance level of .05, can we conclude that the population mean (for those treated with Formulation CS) is less than 7.6 days? Is the sample size large enough to ensure valid inference? If you aren't sure, how would you determine whether or not the sample size was large enough)?
a. Is the sample size large enough to ensure valid inference? If you aren't sure, how would you determine whether or not the sample size was large enough)?
b. State the null and alternative (research) hypotheses.
c. Test the hypothesis using the critical value approach.
d. Test the hypothesis using the p-value approach.
e. Construct and interpret the 90% confidence interval.