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 _______ (b-4) What is your conclusion? We Accept/Reject the null hypothesis.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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 t_calc <______ or t_calc >_______ .

(b-3) Find the test statistic t_calc. (Round your answer to 2 decimal places.)

t_{calc _________}

(b-4) What is your conclusion?

We Accept/Reject the null hypothesis.