(2) One incredibly important aspect of the t-test is that it is very robust with respect to the normality assumption, meaning that the test is (often) still accurate even when the underlying distribution is not normal. Below are density histograms of the t-statistics of 100 samples, each of size 100, pulled three non-normal distributions (uniform[0, 1], Poisson(5), and Exp(1) rep- sectively). 0.35 0.30 03 020 12 0.15 02 0.10 0.05 The first image looks reasonably close to a bell curve, so the use of a t- test here would still yield reasonable conclusions. With the Poisson, there is more departure, but still appropriately close. On the other hand, the exponential distribution is very skewed to the left (think about what the pdf looks like), so we have a relatively larger chance at small samples; this is reflected in the fact that large negative values occur more often than we would expect. 1 2 DUE THURSDAY, 4/1 The moral of the story is: the t-test is a good choice as long as the sample is not too small and the distribution is not too skewed. So on which of the following datasets, if any, would you be hesitant to use a t-test? Explain. (a) (b) (c) (2) One incredibly important aspect of the t-test is that it is very robust with respect to the normality assumption, meaning that the test is (often) still accurate even when the underlying distribution is not normal. Below are density histograms of the t-statistics of 100 samples, each of size 100, pulled three non-normal distributions (uniform[0, 1], Poisson(5), and Exp(1) rep- sectively). 0.35 0.30 03 020 12 0.15 02 0.10 0.05 The first image looks reasonably close to a bell curve, so the use of a t- test here would still yield reasonable conclusions. With the Poisson, there is more departure, but still appropriately close. On the other hand, the exponential distribution is very skewed to the left (think about what the pdf looks like), so we have a relatively larger chance at small samples; this is reflected in the fact that large negative values occur more often than we would expect. 1 2 DUE THURSDAY, 4/1 The moral of the story is: the t-test is a good choice as long as the sample is not too small and the distribution is not too skewed. So on which of the following datasets, if any, would you be hesitant to use a t-test? Explain. (a) (b) (c)