Central Pharmaceuticals, Inc. claims to have a new medication for the common cold— a medication that reduces average recovery time to 80 hours or less. Independent Testing Labs is skeptical and has selected a sample of 50 cold sufferers to whom it administers the new medication. Average recovery time for the sample is 88.4 hours. Assume the population standard deviation is 32.3 hours.
a. Using Central’s claim as the null hypothesis, compute the p-value for the sample result. Is this sample result strong enough to reject Central’s claim at the 1% significance level?
b. Suppose you were to use Independent Testing’s skeptical viewpoint as the null hypothesis (that is, suppose the null hypothesis is 80). Using a 1% significance level, and given the sample results above, what is your conclusion?