A final year student in a Banking and Finance Programme is analysing the sustainability of two commercial banks specialising in mortgage loans. He has collected a 2 sample of 100 borrowers from commercial bank A, and another independent random sample of size 100 borrowers from commercial bank B. From the 2 samples, 30 from commercial bank A, and 50 from commercial bank B paid back the loan on time. Construct a 98.758% CI for π1 − π2.
(d) Times spent by Nursing and Business students studying in the week before the final semester examinations follow a normal distribution. Random samples of size n1 = 15 and n2 = 21 are taken from the two populations in order to estimate the mean study times in the two populations. The population mean study time for SMNS is assumed to be greater than that for SB by 4 hours. Given that the population variances are unknown and are assumed to be different. What is the probability that the difference between the two sample means is less than 17.67225 hours
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