Now we will focus on what happens when we try and use t-methods when the population is heavily skewed and the sample size is small. Similar to question 1, a population was created that was heavily right skewed. Random samples of size 10 were taken and t-statistics for each sample was calculated. The histogram shows how these t-statistics are distributed and a t-distribution density curve is superimposed.

When the population is skewed and the sample size is small, we expect the distribution of sample means to be skewed as well and t-methods should not be used. Do you think it is a good idea to use a t-distribution to estimate the p-value when our sampling distribution is skewed? Explain. Consider describing the difference in p-values one would get when using the density curve compared to the histogram.

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Distribution of t-Statistics small sample from skewed population 0.4 Density 0.2 0. -8 -6 -4 -2 O 2 values of t-statistic