Null & Alternative

An article in Fortune magazine reported on the rapid rise of fees and expenses charged by mutual funds. Assuming that stock fundexpenses and municipal bond fund expenses are each approximately normally distributed, suppose a random sample of 12 stock funds givesa mean annual expense of 1.63 percent with a standard deviation of .31 percent, and an independent random sample of 12 municipal bondfunds gives a mean annual expense of 0.89 percent with a standard deviation of .23 percent. Let µ1 be the mean annual expense for stockfunds, and let µ2 be the mean annual expense for municipal bond funds. Do parts a, b, and c by using the equal variances procedure.Then repeat a, b, and c using the unequal variances procedure.(a)Set up the null and alternative hypotheses needed to attempt to establish that the mean annual expense for stock funds is larger thanthe mean annual expense for municipal bond funds. Test these hypotheses at the .05 level of significance. (Round your sp2 answer to 4decimal places and t-value to 3 decimal places.)H0: µ1 − µ2 ≤ versus Ha: µ1 − µ2 >formula147.mml t =H0 with α = .05(b)Set up the null and alternative hypotheses needed to attempt to establish that the mean annual expense for stock funds exceeds the meanannual expense for municipal bond funds by more than .5 percent. Test these hypotheses at the .05 level of significance. (Round yourt-value to 3 decimal places and other answers to 1 decimal place.)H0: µ1 − µ2versus Ha : µ1 − µ2t =H0 with α = .05(c)Calculate a 95 percent confidence interval for the difference between the mean annual expenses for stock funds and municipal bondfunds. Can we be 95 percent confident that the mean annual expense for stock funds exceeds that for municipal bond funds by more than.5 percent? (Round your answer formula730.mml to 4 decimal places and other answers to 3 decimal places.)The interval = [ , ]., the interval is.5.Redo of (a) for unequal variancesH0: µ1 − µ20 versus Ha: µ1 − µ20formula167.mml = t =t.05 = soH0.Redo of (b) for unequal variancesH0: µ1 − µ2 < .5 versus Ha : µ1 − µ2t = soH0.Redo of (c) for unequal variancesThe interval = [ , ]., the interval is.5.