An economist wants to determine whether average price/earnings (P/E) ratios differ for firms in three industries. Independent samples of five firms in each industry produced the following results after conducting a one-way ANOVA. SSB (sum of squares between groups) = 258.82 and SST (sum of squares total) = 424.04. Based on this information, what conclusion should be reached when testing whether average P/E ratios differ in three industries at the 5% level of significance? Assume that P/E ratios are normally distributed. a. There is sufficient evidence at the 5% level of significance to conclude that not all sample means are equal. b. There is insufficient evidence at the 5% level of significance to conclude that not all population means are equal. c. There is sufficient evidence at the 5% level of significance to conclude that all population means are equal. d. There is sufficient evidence at the 5% level of significance to conclude that not all population means are equal.
Question
An economist wants to determine whether average price/earnings (P/E) ratios differ for firms in three industries. Independent samples of five firms in each industry produced the following results after conducting a one-way ANOVA. SSB (sum of squares between groups) = 258.82 and SST (sum of squares total) = 424.04. Based on this information, what conclusion should be reached when testing whether average P/E ratios differ in three industries at the 5% level of significance? Assume that P/E ratios are normally distributed. a. There is sufficient evidence at the 5% level of significance to conclude that not all sample means are equal.
b. There is insufficient evidence at the 5% level of significance to conclude that not all population means are equal.
c. There is sufficient evidence at the 5% level of significance to conclude that all population means are equal.
d. There is sufficient evidence at the 5% level of significance to conclude that not all population means are equal.
Solution
To answer this question, we need to conduct an F-test using the ANOVA results. However, the information provided is not sufficient to conduct this test. We need the Sum of Squares Within (SSW) and the degrees of freedom within to calculate the Mean Square Within (MSW), and then the F statistic.
The F statistic is calculated as MSB/MSW. Once we have the F statistic, we can compare it with the critical value from the F-distribution table at the 5% level of significance to make a conclusion.
Without these values, we cannot definitively answer this question.
However, if we had these values and found that our calculated F statistic was greater than the critical value from the F-distribution table, we would choose option D: "There is sufficient evidence at the 5% level of significance to conclude that not all population means are equal."
If our calculated F statistic was less than the critical value, we would choose option B: "There is insufficient evidence at the 5% level of significance to conclude that not all population means are equal."
Options A and C are incorrect because they refer to sample means and population means, respectively, and we are conducting a test on population means.
Similar Questions
An economist wants to determine whether average price/earnings (P/E) ratios differ for firms in three industries. Independent samples of five firms in each industry produced the following results after conducting a one-way ANOVA. SSB (sum of squares between groups) = 258.82 and SST (sum of squares total) = 424.04. Based on this information, what would be the exact value of MSB (mean square between)?
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