Problem 2(Calculating sample sizes) A store is interested in estimating the average amount of organic apples sold daily. Apple sales from 40 randomly selected days show a sample average of 83 pounds of apples with a sample standard deviation of 9.2 pounds. Find the sample sizes required to construct 90%, 95%, and 99% condence intervals that estimate the average amount of apples sold daily to Within 10 pounds. Problem 7 (Hypothesis tests and condence intervals) An average lawn has a mean of 21 blades of grass per square inch. A garden store sells an expensive fertilizer designed to transform an average lawn into a lush, thick carpet within three weeks. To test the claim, a random sample of 22 lawn plots was obtained. Each was treated with the fertilizer according to the instructions on the package. Three weeks later the density of each plot was measured by counting the blades of grass per square inch. The summary statistics were 1? = 22.4 and s = 2.7. Conduct a hypothesis test to determine if the fertilizer improves the thickness of a lawn. Report the hypotheses. the test statistic. the p- value, and your conclusion. signicance level a = 0.1