An economist wonders if corporate productivity in some countriesis more volatile than in other countries. One measure of acompany's productivity is annual percentage yield based on totalcompany assets.
A random sample of leading companies in France gave the followingpercentage yields based on assets.
| 4.7 | 5.1 | 3.1 | 3.7 | 2.5 | 3.5 | 2.8 | 4.4 | 5.7 | 3.4 | 4.1 |
| 6.8 | 2.9 | 3.2 | 7.2 | 6.5 | 5.0 | 3.3 | 2.8 | 2.5 | 4.5 |
Use a calculator to verify that the sample variance iss2 ? 2.046 for this sample of Frenchcompanies.
Another random sample of leading companies in Germany gave thefollowing percentage yields based on assets.
| 3.0 | 3.8 | 3.2 | 4.1 | 5.2 | 5.5 | 5.0 | 5.4 | 3.2 |
| 3.5 | 3.7 | 2.6 | 2.8 | 3.0 | 3.0 | 2.2 | 4.7 | 3.2 |
Use a calculator to verify that s2 ? 1.044for this sample of German companies.
Test the claim that there is a difference (either way) in thepopulation variance of percentage yields for leading companies inFrance and Germany. Use a 5% level of significance. How could yourtest conclusion relate to the economist's question regardingvolatility (data spread) of corporate productivity oflarge companies in France compared with companies in Germany? (a)What is the level of significance?
State the null and alternate hypotheses.
Ho: ?12 =?22; H1:?12 >?22Ho:?12 >?22; H1:?12 =?22 Ho: ?22 =?12; H1:?22 >?12Ho:?12 =?22; H1:?12 ??22
(b) Find the value of the sample F statistic. (Use 2decimal places.)
What are the degrees of freedom?
What assumptions are you making about the originaldistribution?
The populations follow independent chi-square distributions. Wehave random samples from each population. The populations followindependent normal distributions. We have random samples from eachpopulation. The populations followindependent normal distributions. The populations follow dependentnormal distributions. We have random samples from eachpopulation.
(c) Find or estimate the P-value of the sample teststatistic. (Use 4 decimal places.)
p-value > 0.200 0.100 < p-value <0.200 0.050 < p-value <0.100 0.020 < p-value < 0.050 0.002 <p-value < 0.020 p-value < 0.002
(d) Based on your answers in parts (a) to (c), will you reject orfail to reject the null hypothesis?
At the ? = 0.05 level, we reject the null hypothesisand conclude the data are not statistically significant. At the? = 0.05 level, we reject the null hypothesis and concludethe data are statistically significant. Atthe ? = 0.05 level, we fail to reject the null hypothesisand conclude the data are not statistically significant. At the? = 0.05 level, we fail to reject the null hypothesis andconclude the data are statistically significant.
(e) Interpret your conclusion in the context of theapplication.
Fail to reject the null hypothesis, there is sufficient evidencethat the variance in percentage yields on assets is greater in theFrench companies. Reject the null hypothesis, there is insufficientevidence that the variance in percentage yields on assets isgreater in the French companies. Reject thenull hypothesis, there is sufficient evidence that the variance inpercentage yields on assets is different in both companies. Fail toreject the null hypothesis, there is insufficient evidence that thevariance in percentage yields on assets is different in bothcompanies.
