06: Do rock music CDs and country music CDs give the consumers the same amount of music listening time? A sample of 12 randomly selected single rock music CDs and a sample of 14 randomly Rock Music Country Music selected single country music CDS 43.0 45.3 have the following total lengths (in 44.3 40.2 minutes). Assume that the two populations are normally 63.8 42.8 distributed with equal standard 32. H 33.0 deviations. a. Compute the value 54.2 33.5 of the test statistic t for testing the null hypothesis that the mean 51.3 37.7 64 8 36.8 lengths of the rock and country music single CDs are the same 36.1 34.6 against the alternative hypothesis that these mean lengths are not 33.9 33.4 51.7 36.5 the same. Use the value of this t statistic to compute the 36.5 43.3 (approximate) p-value. b. Compute the value of the (one-way ANOVA) 59.7 31.7 44.0 test statistic F for performing the test of equality of the mean lengths of 42.7 the rock and country music single CDs and use it to find the (approximate) p-value. c. How do the test statistics in parts a and b compare? How do the p-values computed in parts a and b compare? Do you think that this is a coincidence, or will this always happen