A South African airline serves Spring Water bottles that are supposed to contain an average of 10 ounces (roughly 296 milliliters). A random sample of 12 bottles had the following weights (in ounces). 9.92 9.95 9.94 10.10 10.08 10.04 9.96 10.03 9.98 10.01 9.92 9.89 The sample mean and sample standard deviation are 9.985 and 0.067, respectively. The sample averages for the 4000 bootstrap samples were calculated, and then ordered from smallest to largest. A summary of the ordered averages is given in the following table: Sample No. 1 25 100 200 2000 Sample Ave. 9.927 9.941 9.950 9.956 9.984 Sample No. 2500 3000 3500 3800 1000 Sample Ave. 9.991 9.998 10.006 10.017 10.051 Use the bootstrap results to answer the following questions: (a) Does this sample evidence show that the true mean differs from the bottles' specification of 10 ounces? State the hypotheses to be tested, find the p-value and provide an interpretation. (b) Construct a 90% confidence interval for the population mean based on the bootstrap data provided. (c) Compare the interval obtained in the previous question with a 90% confidence interval ob- tained using standard normal theory. (d) R was used to generate 24 bootstrap samples of size 12 and their means were calculated as shown below: 9.92 9.92 9.95 9.92 10.08 9.94 9.89 9.96 10.01 9.92 10.03 9.96 9.89 9.94 9.98 9.92 9.92 9.92 10.01 9.92 10.03 10.04 9.98 9.98 i) Calculate the bootstrap estimate of the bias of the sample mean. ii) Hence calculate the bootstrap bias corrected mean estimate