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 value of the test statistic used to test whether average P/E ratios differ in the three industries. Assume that P/E ratios are normally distributed. Round your final answer to two decimal places.
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 would be the value of the test statistic used to test whether average P/E ratios differ in the three industries. Assume that P/E ratios are normally distributed. Round your final answer to two decimal places.
Solution
To calculate the test statistic (F statistic) in a one-way ANOVA, we need both the Mean Square Between (MSB) and the Mean Square Within (MSW).
We can calculate the MSB from the information given:
MSB = SSB / (k - 1) = 258.82 / (3 - 1) = 129.41.
However, to calculate the MSW, we need the Sum of Squares Within (SSW), which is not provided in the question.
The SSW can be calculated as follows:
SSW = SST - SSB.
But without the SSW, we cannot calculate the MSW or the F statistic.
So, unfortunately, we cannot calculate the test statistic with the information provided.
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