a) A seed distributor guarantees 95% germination of the seeds he supplies. A retailer has an agreement with the distributor, under which he may test a random sample of 200 seeds for germination and send the whole batch back to the manufacturer if the proportion of germinating seeds is significantly below 95%. With a significance level of 0.1%, what is the smallest number of germinating seeds in a sample of 200 that would be acceptable? If a customer buys 200 of these seeds and finds that 182 seeds actually germinate, determine a 99% confidence interval for the population proportion of germinating seeds.
b) Two different drugs are administered on 2 different sets of 100 patients suffering from the same disease. Their recovery rates are found to be 90 days and 95 days respectively. Construct a 99% confidence interval for the expected difference in the recovery rates.
c) From a random survey of 1515 people in the UK, 606 thought that teachers were underpaid. Determine a 95% confidence interval for the true population of people in the UK who think that teachers are underpaid.
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