Please show all the working for question 3 until question 5. I will definitely give good comments. Please help and thank you in advance

Question 3 (13 marks) Hereditary hemochromatosis (HH) is a recessively inherited genetic disorder resulting from mutations in the HFE gene. There are several possible mutations of different degrees of importance but the disease expresses itself when the C2 82Y allele type is involved in this gene. The condition HH is particularly serious if two such alleles are inherited. It is thought to be particularly prevalent in males with Northern European ancestry. A blood analysis was performed on 1000 Norwegian males. The results showed that 69 of those sampled carried at least one C282Y allele. The proportion of this HFE C282Y allele in the general southern European population (eg Italy] is known to be 3.8%. Perform a test of signicance at 5% to determine if the proportion of HFE gene is greater in the Northern European male population. Show all steps clearly. Question 4 (15 marks) In the article \"Evaluation variability in lling operations\" (Food Technology [1984]: 51-55], a packaging process for ground beef was considered over a series of days. An important question is whether the true mean amount delivered by this process changes from day to day. Ten packages were accurately weighed and randomly selected over the course of the day. This was done on different packages also on the consecutive day. The results were: 1397. 8 1394.8 1385. 3 1391. 7 1400.1 1391.2 1393. 5 1385. 7 1384.0 1391.0 1410. 0 1393.9 1402. 5 1405. 9 1399. 9 1404.2 1398.5 1387.3 1391.8 1392.5 a) Are these data paired or independent samples? b] State the summary statistics associated with the data above. c] Test the hypothesis that the true mean amount changes from the rst day to the second day. Use a signicance level of 0.05. Show all steps clearly. Question 5 (15 marks) A study reported the results of its annual travel manager salary and attitude survey. One question asked for the travel professional's opinion on the fairness of his /her salary. Responses were classied as \"salary too low,\" \"equitable/fair,\" or "paid well.\" The table below gives a breakdown of the res .onses in each cate o b - ender. m a] Find the conditional distributions of travel professional's opinion for each gender. Do you think the opinion on fairness of a travel professional's salary differs for males and females? Explain why. b] Conduct the appropriate statistical test using a level of signicance 5% to decide if the opinion on fairness of a travel professional's salary differs for males and females. Question 5 (15 marks) A study reported the results of its annual travel manager salary and attitude survey. One question asked for the travel professional's opinion on the fairness of his /her salary. Responses were classied as \"salary too low,\" \"equitable/fair,\" or "paid well." The table below gives a breakdown of the res nonses in each cate o b -ender. a) Find the conditional distributions of travel professional's opinion for each gender. Do you think the opinion on fairness of a travel professional's salary differs for males and females? Explain why. b] Conduct the appropriate statistical test using a level of signicance 5% to decide if the opinion on fairness of a travel professional's salary differs for males and females. Page 2 of 3 Question 6 [10 marks) Many cheeses are produced in the shape of a wheel. Because of slight variations in the consistency of a cheese, the average weight varies from wheel to wheel. The production output is supposed to have an average weight of at least 500g per wheel and samples are taken to check this. One random sample of 16 wheels of Brie cheese had a mean weight of 515.5 grams with a standard deviation of 66.5 grams. The populations of the cheeses are known to have a normal distribution of weights. 3] Find the point estimate of the mean weight of cheese wheel. b) Find and interpret the 90% condence interval for the mean weight of cheese wheel. c] Use your answer in b) to determine if the sample shows that the production output does not have the correct average weight per wheel. d] To halve the margin of error for the sample above, what sample size would be required