The annual dividend rates for a random sample of 16 companies in three different
ID: 3056593 • Letter: T
Question
The annual dividend rates for a random sample of 16 companies in three different industries, construction, architecture, and engineering, were recorded. The ANOVA comparing the mean annual dividend rate among three industries rejected the null hypothesis that the dividend rates were equal. The mean square error (MSE) was 3.36. The following table summarized the results:
When comparing the mean annual dividend rate for companies in the construction and engineering industries, which is the 95% confidence intervals?
Construction Architecture Engineering Number Sampled Mean Annual Dividend Rate 11.62 15.4 17.4Explanation / Answer
Denote 1 and 2 as the mean dividend rate of companies’ construction and engineering respectively. The our aim is to find the 95% CI for 1 - 2
The 95% CI is given by,
( Xbar – Ybar – T * (MSE*(1/n+1/m) , Xbar – Ybar + T * (MSE*(1/n+1/m))
(11.62-17.4-2.16037 *3.36*(1/5+1/6), 11.62-17.4-2.16037 *3.36*(1/5+1/6))
(-8.17791, -3.38209) Here T is the value of T distribution with error df = 13 and = 0.05.
As 1 - 2 =0 is not included in the 95% CI one can conclude that mean dividend of construction and engineering companies are different.
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