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A random sample of 30 words from Jane Austen’s Pride and Prejudice had a mean length of 4.08 letters with a standard deviation of 2.40. A random sample of 30 words from Henry James’s What Maisie Knew had a mean length of 3.85 letters with a standard deviation of 2.26. Which of the following is a correct expression for the 95% confidence interval for the difference in mean word length for these two novels?​

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Answer:

The confidence interval will be computed using either the Z or t distribution for the selected confidence level and the standard error of the point estimate. The use of Z or t again depends on whether the sample sizes are large (n1 > 30 and n2 > 30) or small. The standard error of the point estimate will incorporate the variability in the outcome of interest in each of the comparison groups. If we assume equal variances between groups, we can pool the information on variability (sample variances) to generate an estimate of the population variability. Therefore, the standard error (SE) of the difference in sample means is the pooled estimate of the common standard deviation (Sp) (assuming that the variances in the populations are similar) computed as the weighted average of the standard deviations in the samples, i.e.:

Explanation:

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