2. At the Hawaii Pineapple Company, managers are interested in the size of the pineapples grown in the companys fields. Last year, the weight of the pineapples harvested from one large field was roughly normally distributed with a mean of 31 ounces and a standard deviation of 4 ounces. A different irrigation system was installed in this field after the growing season. Managers wonder if the the mean weight of pineapples grown in the field this year will be different from last. (a) Write out the managers question in terms of a null (Ho) and alternative (HA) hypotheses about the population mean weight u of all pineapples for this year. (b) The managers would like to design a test that can detect a mean increase of 2 ounces (MA = 33). Identify the null and alternative distributions of X from a sample of 30 pineapples. (c) If the managers choose to use a significance level of 0.10 and assume o = 4, identify the power of a Z test to detect a mean increase of 2 ounces (MA = 33). They plan to look at a sample of 30 pineapples this year and do a two-sided hypothesis test. Also identify the probability of making a type 2 error if the true average weight in this years crop is 33 ounces, MA = 33. (d) What sample size should the managers use to ensure their a = 0.1, 2-sided Z test has power of at least 0.9 to detect a true mean of 33 ounces (assuming o = 4)? 3. The managers at the Hawaii Pineapple Company collect a sample of size 51 from their field this year to test the hypotheses: Ho : M = 31 versus HA : M # 31 at a 10% significance level (a = 0.1). They still believe it is reasonable to assume the distribution of weights for the pineapples is approximately normal, but they are not going to assume they know o. The collected pineapple weights can be found in the file Pineapples . CSV. (a) Create a histogram and a qq-plot of the data. Does the normality assumption appear to be appropriate? (b) Compute a t test statistic and p value "by hand" and draw a conclusion for the hypothesis test at a 10% level. (c) Verify your answer to (b) with the t. test function. (d) Build a 90% t CI on the pineapple data. Does this interval cover Mo = 31? How does this correspond with the results of the t test