please solve parts d e f
Extracted text: 5. A random sample of 30 males between ages 25 – 40 is taken for a health and fitness study. Following are their wieghts in kilograms: 75, 72, 83, 76, 65, 88, 67, 76, 78, 89, 86, 74, 78, 89, 88, 78, 77, 83, 84, 69, 72, 74, 78, 75, 61, 86, 85, 84, 81, 79 It was also asked of them if they exercise daily, and only 13 of them answered yes. Based on the above sample data: (a) What can you conclude about the average weight of males aged 25 – 40 years at 90% confidence level? (b) What is the interval for average weight of this population if you want to make a claim at 98% confidence level? (c) What is the proportion of this population that exercises daily? Give a 95% confidence interval. (d) Now the tricky part: Suppose it is known that the average weight of this population is exactly 80 kg. Based on the above sample, what would be the proportion of this population that has a weight higher than 86 kg with a confidence level of 95%. Give a confidence interval for this proportion at this confidence level. ( Hint: Find out the confidence interval for the population standard deviation first). (e) Now suppose that it is instead given that the standard deviation of this population is 6 kg but the average is unknown. Based on the above sample, how would your confidence intervals change now at 90% and 98% level. (f) Again, assuming that the standard deviation is known to be 6 kg, if you want to estimate the average weight of this population within 1 kg, what should be your minimum sample size? Assume throughout that the population weights are distributed normally.