A stock analyst randomly selected stocks in each of three industries and compile
ID: 3128316 • Letter: A
Question
A stock analyst randomly selected stocks in each of three industries and compiled the five-year rate of return for each stock. The data are shown in the table below:
Financial
Energy
Utilities
10.76
6.45
15.05
13.91
3.95
8.16
20.73
7.12
19.50
9.60
15.70
6.75
18.79
8.47
11.38
7.22
9.25
21.01
12.04
14.40
mean
11.93
14.80
9.00
std. dev.
4.69
5.06
3.87
We would like to conduct an analysis of variance at the 1% level of significance to determine whether there is a difference in the true mean return for the three industries.
(a) What assumptions must be made in order for our inference procedures to be valid?
(b) State the hypotheses for the appropriate test of significance.
(c) Do all necessary calculations to construct an ANOVA table. Show all calculations as well as the completed table.
(d) What is the P-value of the test? What is your conclusion?
(e) Give an interpretation of the P-value calculated in (f).
(f) Verify your results by conducting the appropriate hypothesis test in JMP. To do this, create a column called Return and enter all 21 data values in this column (all 6 data values for Financial Stocks, all 8 data values for Energy Stocks and then all 7 data values for Utilities Stocks). Create a second column called Industry and type F in the first 6 rows (beside the data values for the Financial Stocks), type E in the next 8 rows (beside the data values for the Energy Stocks) and type U in the next 7 rows (beside the data values for the Utilities Stocks). Go to Analyze > Fit Y by X. Choose Return as Y and Industry as X. Click OK. Now, under the red arrow, selectMeans/Anova.
What is the exact P-value of the test?
(g) Suppose you had instead used the critical value method to conduct the test. What would be the decision rule and the conclusion?
Financial
Energy
Utilities
10.76
12.726.45
15.05
13.91
3.95
8.16
20.73
7.12
19.50
9.60
15.70
6.75
18.79
8.47
11.38
7.22
9.25
21.01
12.04
14.40
mean
11.93
14.80
9.00
std. dev.
4.69
5.06
3.87
Explanation / Answer
A stock analyst randomly selected stocks in each of three industries and compiled the five-year rate of return for each stock. The data are shown in the table below:
alpha = level of significance = 1% = 0.01
Assumptions for ANOVA :
i) Each of k-groups of measurements is from a Normal population.
ii) Each group is randomly selected and independent of all other groups.
iii) Variables from each group come from distributions with approximately the same standard deviation.
Here the hypothesis for the test is,
H0 : mu1 = mu2 = mu3 Vs H1 : Atleast one mean is differ than 0.
We conduct ANOVA by using EXCEL.
Steps are :
Enter all the data in EXCEL sheet --> Data --> Data Analysis --> Anova: Single Factor --> ok --> Input Range : select all the data --> Grouped by: Columns --> Alpha : 0.01 --> Output Range : select one empty cell --> ok
Output is as follows :
Test statistic F = 2.98369
And P-value = 0.076
P-value > alpha
Accept H0 at 1% level of significance.
Conclusion : Three population means are equal.
Anova: Single Factor SUMMARY Groups Count Sum Average Variance Column 1 6 71.6 11.93333 21.95119 Column 2 8 118.38 14.7975 25.63199 Column 3 7 62.98 8.997143 15.00239 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 125.7109 2 62.85544 2.98369 0.076009 6.012905 Within Groups 379.1942 18 21.06635 Total 504.9051 20Related Questions
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