Suppose I surveyed a random sample of commuters who had jobs in Manhattan, 51 whose primary mode of transportation was bus (B) or subway (S) and 80 whose primary mode was Metro-North (MN) or the Long Island Railroad (LIRR). Of the 51 in the first group, the mean annual income was $40,000 with a standard deviation of $5,100; of the 80 in the latter group, the mean annual income was $60,000 with a standard deviation of $8,000. (a) Based solely on your calculations, according to this confidence interval, can we reject the null hypothesis? Put differently, can we say the two groups’ mean income levels in the population differ? How do you know? (b) If we were to test our null hypothesis with a 99% confidence interval, how would that interval compare to the 95% interval you already calculated? Would you expect the new (99%) confidence interval to be (I) narrower (ii) wider (iii) the same?
Suppose I surveyed a random sample of commuters who had jobs in Manhattan, 51 whose primary
(a) Based solely on your calculations, according to this confidence interval, can we reject the null hypothesis? Put differently, can we say the two groups’ mean income levels in the population differ? How do you know?
(b) If we were to test our null hypothesis with a 99% confidence interval, how would that interval compare to the 95% interval you already calculated? Would you expect the new (99%) confidence interval to be
(I) narrower
(ii) wider
(iii) the same?
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