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

Choose the appropriate hypotheses. Assume σ_A² is the variance of the Portfolio A and σ_B² is the variance of the Portfolio B.

• H₀: σ_A²/σ_B² ≤ 1 versus H₁: σ_A²/σ_B² > 1

• H₀: σ_A²/σ_B² = 1 versus H₁: σ_A²/σ_B² ≠ 1

• H₀: σ_A²/σ_B² ≥ 1 versus H₁: σ_A²/σ_B² < 1

(a-2) Specify the decision rule. (Round your answers to 2 decimal places.)

Reject the null hypothesis if F_calc > _________ .

(a-3) Calculate the test statistic F_calc. (Round your answer to 2 decimal places.)

F_{calc = _____________}


(b-1) Choose the appropriate hypotheses. Assume d = company assessed value – employee assessed value.

• 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 = ________}

Answer 1