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

 Click here for the Excel Data File
 
(a-1) Choose the appropriate hypotheses. Assume σ_A² is the variance of the Portfolio A and σ_B² is the variance of the Portfolio B.
 

multiple choice 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

• 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 > 3.47  Numeric ResponseEdit Unavailable. 3.47 correct..

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

 

F_calc           9.86 Numeric ResponseEdit Unavailable. 9.86 correct.

 
(a-4) What is your conclusion?

 

We reject  Correct the null hypothesis.

 

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

 

multiple choice 2

• 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           0.490 Numeric ResponseEdit Unavailable. 0.490 correct.

 
(b-4) What is your conclusion?

 

We fail to reject  Correct the null hypothesis.