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 Questions: (a-1) Choose the appropriate hypotheses. Assume σA2 is the variance of the Portfolio A and σB2 is the variance of the Portfolio B. multiple choice 1 H0: σA2/σB2 ≤ 1 versus H1: σA2/σB2 > 1 - Correct Answer H0: σA2/σB2 = 1 versus H1: σA2/σB2 ≠ 1 H0: σA2/σB2 ≥ 1 versus H1: σA2/σB2 < 1 (a-2) Specify the decision rule. (Round your answers to 2 decimal places.) Reject the null hypothesis if Fcalc > _______ (correct answer 3.47). (a-3) Calculate the test statistic Fcalc. (Round your answer to 2 decimal places.) Fcalc ___________ (correct answer 9.86) (a-4) What is your conclusion? We _________ (correct answer Reject) the null hypothesis. (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 - Correct Answer 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 > _____?______ . (This is where I need help) (b-3) Find the test statistic tcalc. (Round your answer to 2 decimal places.) tcalc __________ (correct answer .49) (b-4) What is your conclusion? We _________ (correct answer Fail to Reject) the null hypothesis.
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 |
Questions:
(a-1) Choose the appropriate hypotheses. Assume σA2 is the variance of the Portfolio A and σB2 is the variance of the Portfolio B.
multiple choice 1
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H0: σA2/σB2 ≤ 1 versus H1: σA2/σB2 > 1 - Correct Answer
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H0: σA2/σB2 = 1 versus H1: σA2/σB2 ≠ 1
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H0: σA2/σB2 ≥ 1 versus H1: σA2/σB2 < 1
(a-2) Specify the decision rule. (Round your answers to 2 decimal places.)
Reject the null hypothesis if Fcalc > _______ (correct answer 3.47).
(a-3) Calculate the test statistic Fcalc. (Round your answer to 2 decimal places.)
Fcalc ___________ (correct answer 9.86)
(a-4) What is your conclusion?
We _________ (correct answer Reject) the null hypothesis.
(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 - Correct Answer
-
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 > _____?______ . (This is where I need help)
(b-3) Find the test statistic tcalc. (Round your answer to 2 decimal places.)
tcalc __________ (correct answer .49)
(b-4) What is your conclusion?
We _________ (correct answer Fail to Reject) the null hypothesis.
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