P S4R EoM Exam Style Question Topic 9 t9 exstyle The Calcium content of soy milk is approximately normally distributed within the same brand of soy milk. The Calcium content of two random samples of 13 PlantPower soy milk boxes are recorded in Sample A and Sample B. Sample C records the Calcium content of a random sample of 13 boxes from another brand, HealthFit. All measurements are mg/100g. Sample data: t9 exstyle.mat. (a) Use Samples A and B to construct 99% confidence intervals for the mean Calcium content of PlantPower soy milk. Compare the margins of error and explain why is one much bigger than the other. (5 marks) (b) What range of confidence levels would reduce the margin of error of the Sample B confidence interval below 0.50 mg? (5 marks) (c) Find the range of confidence levels so that the Sample A and Sample B confidence intervals do not overlap. (6 marks) (d) Use Samples A and C to construct a 95% confidence interval for the difference in mean Calcium content between the PlantPower and HealthFit brands. (i) Does this confidence interval provide reliable evidence to suggest which brand has a higher average Calcium content? (ii) Give an example of a confidence level at which the difference is significantly different from zero and explain if the corresponding confidence interval is useful. (7 marks) (e) Explain why the assumption that the Calcium content is normally distributed is important in this problem. (2 marks) (Total: 25 marks)

























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