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

(a-1) Choose the appropriate hypotheses. Assume σA2 is the variance of the Portfolio A and σB2 is the variance of the Portfolio B.

H0: σA2/σB2 ≤ 1 versus H1: σA2/σB2 > 1

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> .

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

Fcalc

(a-4) What is your conclusion?

We (Click to select) the null hypothesis.

(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 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 (Click to select) the null hypothesis