Please help **Rates of Return Analysis in Investment Portfolios**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." At a significance level of α = 0.025, does the sample show that portfolio A has significantly greater variance in rates of return than portfolio B? At α = 0.025, is there a significant difference in the means?**Portfolio Data:**| Portfolio A | Portfolio B ||-------------|-------------|| 5.27 | 9.16 || 10.83 | 8.59 || 12.47 | 7.98 || 4.18 | 6.58 || 5.66 | 7.34 || 8.86 | 7.13 || 7.72 | 7.65 || 9.72 | 7.66 || 9.66 | 8.73 || 4.82 | 8.85 || 11.56 | 7.73 || 11.46 | 9.97 |**Step-by-Step Analysis:**1. **Choose the Appropriate Hypotheses:** Assume \(\sigma_A^2\) is the variance of Portfolio A and \(\sigma_B^2\) is the variance of Portfolio B. - \( H_0: \frac{\sigma_A^2}{\sigma_B^2} = 1 \) versus \( H_1: \frac{\sigma_A^2}{\sigma_B^2} > 1 \) - \( H_0: \frac{\sigma_A^2}{\sigma_B^2} = 1 \) versus \( H_1: \frac{\sigma_A^2}{\sigma_B^2} \neq 1 \) - \( H_0: \frac{\sigma_A^2}{\sigma_B^2} = 1 \) versus \( H_1: \frac{\sigma_A^2}{\sigma_B^2} < 1 \)2. **Specify the Decision Rule (Round Your Answer to 2 Decimal Places):** - Reject the null hypothesis if \( F ### Statistical Analysis Exercise**(a-4) What is your conclusion?**We [Click to select] the null hypothesis.**(a-1) Choose the appropriate hypotheses. Assume \(d = \text{company assessed value} - \text{employee assessed value}\).**- \(H_0: \mu_1 - \mu_2 = 0\) vs. \(H_1: \mu_1 - \mu_2 \neq 0\)- \(H_0: \mu_1 - \mu_2 \ge 0\) vs. \(H_1: \mu_1 - \mu_2 < 0\)- \(H_0: \mu_1 - \mu_2 \le 0\) vs. \(H_1: \mu_1 - \mu_2 > 0\)**(b-2) State the decision rule for 0.025 level of significance. (Use the quick rule for the degree of freedom. Round your answers to 3 decimal places. A negative value should be indicated by a minus sign.)**Reject the null hypothesis if \( t_{\text{calc}} < \) [Blank] or \( t_{\text{calc}} > \) [Blank].**(b-3) Find the test statistic \( t_{\text{calc}} \). (Round your answer to 2 decimal places.)**\( t_{\text{calc}} \) [Blank]**(b-4) What is your conclusion?**We [Click to select] the null hypothesis.

Solution: Given information: n1= 12 Sample size of An2= 12 Sample size of B x1= 8.4925 Sample mean of Ax2=8.1192 Sample mean of B s12= 8.5650 Sample variance of A s22=0.9289 Sample variance of B α= 0.025 Level of significance a-1) The null and alternative hypotesis is Ho:σ2Aσ2B≤1 VS Ha:σ2Aσ2B>1 Option A is Correct a-2) The critical value at α=0.025 is Fα, n1-1, n2-1=F0.025,11,11= 3.47 From F table Decision Rule: Reject the null hypothesis if Fcal > 3.47 a-3) Test statistic Fcalc=s12s22Fcalc=8.56500.9289Fcalc= 9.22 Test statistic Fcalc = 9.22 a-4) Conclusion: We should reject the null hypothesis b-1) The null and alternative hypothesis is Ho:μ1-μ2=0 VS Ha:μ1-μ2≠0 Option A is Correct b-2) To find degree of freedom Degree of freedom =df=Min(n1-1, n2-1)df= min(12-1, 12-1)= 11 The critical values at α=0.025 are -tα/2,df=t-0.0125,11= -2.593 From Excel and tα/2,df=t0.0125, 11= 2.593 From Excel The critical values are -2.593 and 2.593 Decision Rule : Reject the null hypothesis if tcalc < -2.593 or tcalc > 2.593 b-3) Test statistic tcalc= x1-x2s12n1+s22n2tcalc=8.4925-8.11928.565012+0.928912tcalc=8.4925-8.11920.71375+0.077408tcalc=8.4925-8.11920.791158tcalc=0.37330.889471= 0.419688tcalc=0.42 Test statistic tcalc= 0.42 b-4) Conclusion: We fail to reject the null hypothesis.

Math

Statistics

Rates of return (annualized) in two investment portfolios are compared over the last 12 quarters. They are considered similar in safety. but portfolio Bis advertised as being "less volatile." (a) At a = .025, does the sample show that portfolio A has significantly greater variance in rates of return than portfolio ? (b) At a = .025, is there a significant difference in the means? Portfolio B 9.10 Portfolio A 5.27 18.83 8.69 12.47 7.70 4.10 6.58 5.66 7.54 8.66 7.13 7.70 7.65 9.72 7.66 9.66 8.73 4.82 8.95 11.56 7.73 11.46 9.97 Dpicture Click here for the Excel Data File (a-1) Choose the appropriate hypotheses. Assume o,2 is the variance of the Portfolio A and og? is the variance of the Portfolio B. Ho: 0Aiog2s1 versus H: OA2ior?>1 Ho: OA2I0B2 = 1 versus H: OA2iog? 1