Rates of return (annualized) in two investment portfolios are compared over the last 12 quarters. They are considered similar in safety, but portfolio B is advertised as being “less volatile.” (a) At α = .025, does the sample show that portfolio A has significantly greater variance in rates of return than portfolio B? (b) At α = .025, is there a significant difference in the means? Portfolio A Portfolio B 5.23 8.96 10.91 8.60 12.49 7.61 4.17 6.60 5.54 7.77 8.68 7.06 7.89 7.68 9.82 7.62 9.62 8.71 4.93 8.97 11.66 7.71 11.49 9.91 (b-1) Choose the appropriate hypotheses. Assume d = company assessed value – employee assessed value. multiple choice 3 H0: μ1 – μ2 = 0 vs. H1: μ1 – μ2 ≠ 0 H0: μ1 – μ2 ≥ 0 vs. H1: μ1 – μ2 < 0 H0: μ1 – μ2 ≤ 0 vs. H1: μ1 – μ2 > 0 (b-2) State the decision rule for .01 level of significance. (Round your answers to 3 decimal places. A negative value should be indicated by a minus sign.) Reject the null hypothesis if tcalc <______?____ or tcalc > _____?______ . (b-3) Find the test statistic tcalc. (Round your answer to 2 decimal places.) tcalc
Rates of return (annualized) in two investment portfolios are compared over the last 12 quarters. They are considered similar in safety, but portfolio B is advertised as being “less volatile.” (a) At α = .025, does the sample show that portfolio A has significantly greater variance in rates of return than portfolio B? (b) At α = .025, is there a significant difference in the means?
Portfolio A | Portfolio B |
5.23 | 8.96 |
10.91 | 8.60 |
12.49 | 7.61 |
4.17 | 6.60 |
5.54 | 7.77 |
8.68 | 7.06 |
7.89 | 7.68 |
9.82 | 7.62 |
9.62 | 8.71 |
4.93 | 8.97 |
11.66 | 7.71 |
11.49 | 9.91 |
(b-1) Choose the appropriate hypotheses. Assume d = company assessed value – employee assessed value.
multiple choice 3
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H0: μ1 – μ2 = 0 vs. H1: μ1 – μ2 ≠ 0
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H0: μ1 – μ2 ≥ 0 vs. H1: μ1 – μ2 < 0
-
H0: μ1 – μ2 ≤ 0 vs. H1: μ1 – μ2 > 0
(b-2) State the decision rule for .01 level of significance. (Round your answers to 3 decimal places. A negative value should be indicated by a minus sign.)
Reject the null hypothesis if tcalc <______?____ or tcalc > _____?______ .
(b-3) Find the test statistic tcalc. (Round your answer to 2 decimal places.)
tcalc
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