3. Refer to exercise 10.137 starting on page 579 of the textbook. Below is Minit

Question

3. Refer to exercise 10.137 starting on page 579 of the textbook. Below is Minitab output, including descriptive statistics for each of the five boreholes as well as the ANOVA table for comparing the mean Al/Be ratio among the five different boreholes. Based on the ANOVA table, we see that the one-way ANOVA hypothesis F-test results in a p-value of o001, thus the results of this analysis are significant and we can conclude that the population mean AVBe ratio differs least two boreholes At the a 10 significance level, perform the Bonferroni for at multiple comparisons procedure to determine which pairs of means (f any) are significantly different. Interpret the fin results within the context of he problem. NOTE: You DO NOT need to perform a hypothesis test for this problem. You only need to perform the multiple comparisons procedure.

Explanation / Answer

1. Fill up n-1 and variance (sd^2)

Now we are making comparison between each pair among the 5 groups i.e 5C2 combinations which is 10.

2. Calculate pooled variance, Sp as

sum[ (ni - 1) SDi^2 ] / sum (ni-1)

3. Find the difference in means and absolute difference in means for each of the pairs

4. Calculate critical value as t(alpha/10, 26) * Sp * sqrt(1/n1+1/n2) for each of the pairs

(alpha/10 - because we are making 10 comparisons and hence correcting the alpha value, 26 as sum of all n )

5. compare with absolute difference in means, if it is lower than critical value there is no signifcance

Alternate method is find Lconf limit as (diff in mean - critical value) and Uconf limit as (diff in mean +critical value). If this range (lconf, uconf) has 0 in between, then it is not signifcant.

Sp pooled variance = 0.201278

t(0.01,26) =T.INV.2T(0.01,26)= 2.7787

n mean sd n-1 sd^2 umrb-1 7 3.497 0.364 6 0.1325 umrb-2 6 4.017 0.573 5 0.3283 umrb-3 7 3.761 0.483 6 0.2333 swra 3 2.643 0.358 2 0.1282 sd 3 2.78 0.259 2 0.0671 df 26

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