Question

A small independent stock broker has created four sector portfolios for her clients. Each portfolio always has five stocks that may change from year to year. The volatility of each stock is recorded for each year. Are the main effects significant?

	Health	Energy	Retail	Leisure
2013	17.5	24.9	23.0	22.1
	19.5	21.4	21.5	25.1
	16.0	26.0	20.2	21.5
	13.9	21.8	13.3	20.6
	17.9	21.1	19.5	19.4
2015	24.3	21.8	25.5	24.9
	30.6	22.4	29.0	28.0
	24.1	21.6	25.6	27.4
	27.5	21.3	25.7	24.9
	24.2	20.2	28.5	28.0
2017	20.5	23.5	22.9	21.8
	22.7	19.1	23.5	28.6
	19.5	25.6	27.8	21.7
	17.3	17.3	17.1	17.2
	21.7	27.8	25.7	19.8

Based on these sample data and using a significance level of 0.01, what conclusions should be reached?

1. How many blocks were used in this study?

2. How many populations (treatments) are involved in this test?

3. Is there a significant interaction between sector and year? Use a significance level of 0.01

a. What are your hypothesis statements?

b. What is your critical value?

c. What is your test statistic?

d. What is your decision regarding the null hypothesis? Interpret the result.

4. Compare the mean difference in volatility by sector: Use a significance level of 0.01

a. What are your hypothesis statements?

b. What is your critical value?

c. What is your test statistic?

d. What is your decision regarding the null hypothesis?

5. Compare the mean difference in volatility by year: Use a significance level of 0.01

a. What are your hypothesis statements?

b. What is your critical value?

c. What is your test statistic?

d. What is your decision regarding the null hypothesis?

Answer 1

1)

there are 3 blocks in the study (2013,2015,2017)

2) there are 4 treatments..(Health   Energy   Retail   Leisure)

3)

null hypothesis: there is not a significant interaction between sector and year

alternative hypothesis: there is a significant interaction between sector and year

Anova: Two-Factor With Replication

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	253.764	2.000	126.882	15.218	0.000	3.191
Columns	48.197	3.000	16.066	1.927	0.138	2.798
Interaction	182.932	6.000	30.489	3.657	0.005	2.295
Within	400.196	48.000	8.337
Total	885.089	59.000

3) b)

critical value = 2.295

c)

F test = 3.657

d)

Ftest> critical , reject null hypothesis

there is a significant interaction between sector and year

...........................

4) Ho : there is no difference in the mean in volatility by sector

H1 : there is difference in the mean in volatility by sector

b)

critical value = 3.191

c)

Ftest : 15.218

d)

Ftest > critical value , so reject null hypothesis

so,

there is difference in the mean in volatility by sector

5)

Ho: there is no mean difference in volatility by year

H1: there is mean difference in volatility by year

b)

critical value = 2.798

c)

Ftest = 1.927

d)

Ftest < critical value , do not reject null hypothesis

so,

there is no mean difference in volatility by year

please revert back for doubt