Question

3. An article in Fortune magazine reported on the rapid rise of fees and expenses charged by mutual funds. Assuming that stock fund expenses and municipal bond fund expenses are each approximately normally distributed, suppose a random sample of 12 stock funds gives a mean annual expense of 1.63 percent with a standard deviation of 0.31, and an independent random sample of 12 municipal bond funds gives a mean annual expense of 0.89 percent with a standard deviation of 0.23. Let 1 be the mean 2 annual expense for stock funds and let hy be the mean for municipal bond funds. Assume equal population variances and test the claim that the mean annual expense for stock funds is larger than that for municipal bond funds. Is this an one-sample or two-sample test? Is this test for population mean or proportion? Is this a large sample or small sample? State the null and alternative hypotheses: is this a left-, right-, or two-tailed test? * Find the critical value(s) at 0.05 level of significance. Compute the pooled standard deviation 8p: Compute the test statistic. Decision: do you reject or fail to reject the null hypothesis? State your conclusion to the original research question:

Answer 1

Given that, n = 12, X = 1.63, S, = 0.31 ₂ = 12, X = 0.89, 52 = 0.23 • This is a towo - sample test This is test for mean pop wation This is a small sample test * Null & alternative Hypothesis :- Ho: 41 = 42 VIS Hi : ei u2 This is right tailed test . Critical value = tnitne-2,5 =+12+12-2,0.05 t22, = 10717 0.05 { Using t-table Pooled S.O. Sp= (min) 5,²+ + (02-1) 5² n, th2-2 (11 x 0.31 ) + (11X0-23) 12+12-2 0.2729 test statistic it t lo 63 - 0.89 Sp ttt n2 0:27 29 ( 1 - 2 + 1 - 2 t - 6.642 Decision :- Here, t > Reject tn, 2-2,4 the i. e., 6.6427 1.717 mull Hypothesis. Conclusion :- There Claim that the mean is sufficient evidence to support the annual expense for stock funds is municipal bond hund, larger than that of