In a children’s book, the mean word length is 3.6 letters with a standard deviation of 2.1 letters. In a novel aimed at teenagers, the mean word length is 4.4 letters with a standard deviation of 2.4 letters. Both distributions of word length are unimodal and skewed to the right. Independent random samples of 40 words are selected from each book. Let xC represent the sample mean word length in the children’s book and let xT represent the sample mean word length in the teen novel. Find the mean of the sampling distribution of xC-xT
Calculate and interpret the standard deviation of the sampling distribution. Verify that the 10% condition is met.
Justify that the shape of the sampling distribution is approximately Normal.
What is the probability that the sample mean word length is greater in the sample from the children’s book than in the sample from the teen novel?