Question 9.7: In Example 9.4 (in Section 9.1), several measurements of the......

ISE Principles of Statistics for Engineers and Scientists [987713]

In Example 9.4 (in Section 9.1), several measurements of the maximum hourly con-centrations (in 𝜇g/m³) of $SO_{2}$ were presented for each of four power plants, and it was concluded that the mean concentrations at the four plants were not all the same. The following output (from MINITAB) presents the Tukey–Kramer 95% simultaneous con-fidence intervals for mean concentrations at the four plants. Which pairs of plants, if any, can you conclude with 95% confidence to have differing means?

Tukey 95% Simultaneous Confidence Intervals All Pairwise Comparisons

Individual confidence level = 98.87%

1 subtracted from:

—–+———+———+———+—-				Upper	Center	Lower
(——–*——–)				661.1	385.3	109.4	2
(——–*———)				603.1	312.3	21.4	3
(——–*——–)				436.4	170.9	-94.6	4
—–+———+———+———+—- -300 0 300 600

2 subtracted from:

—–+———+———+———+—-				Upper	Center	Lower
(———*——–)				202.9	-73.0	-348.9	3
(———*——–)				34.7	-214.3	-463.4	4
—–+———+———+———+—- -300 0 300 600

3 subtracted from:

—–+———+———+———+—-				Upper	Center	Lower
(——–*——–)				124.1	-141.3	-406.8	4
—–+———+———+———+—- -300 0 300 600

Step-by-Step

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Among the simultaneous confidence intervals, there are two that do not contain 0. These are the intervals for $\mu_{1}\ −\ \mu_{2}$ and for $\mu_{1}\ −\ \mu_{3}$ . Therefore we conclude that the mean concentrations differ between plants 1 and 2 and between plants 1 and 3.

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