Question

# The “fog index” is used to measure the reading difficulty of a written text. Suppose random...

The “fog index” is used to measure the reading difficulty of a written text. Suppose random samples of 10 pages of material from Wall Street Journal and Sports Illustrated had the following sample results:

WSJ: Mean: 60.70 std dev: 9.3814237 Min: 44 Max: 75 N 20

SI: Mean: 43.1 Std Dev: 6.4195881 Min: 34 Max: 51 N: 16

Suppose we wish to test if the population mean fog index for the Wall Street Journal is different than the population mean fog index for Sports Illustrated, that is, ?0: ?WSJ = ?SI vs. ?1: ?WSJ ≠ ?SI, at the 5% level of significance. For parts (a) and (b), conduct your analysis based on simple approximation of degrees of freedom shown in lecture. For all parts, do not assume underlying equal variances. a) Hand compute the test statistic and conduct the test of hypotheses using the critical value approach. Show all your computations. What do you conclude and why? b) Find out the p-value for testing the hypothesis. what do you conclude and why?

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