PERFORM THE APPROPRIATE ANALYSIS, BEING CAREFUL TO STATE HYPOTHESES AND DECISION
ID: 3173406 • Letter: P
Question
PERFORM THE APPROPRIATE ANALYSIS, BEING CAREFUL TO STATE HYPOTHESES AND DECISION RULE. LASTLY, APPLY Tukey's HSD. Low Pb [Use random sample of size 13 for this level!] 85 90 107 85 100 97 101 64 111 100 76 736 100 90 135 104 149 99 113 104 101 111 118 99 122 87 118 113 128 121 111 104 51 100 113 82 146 107 83 108 93 114 113 94 106 92 79 129 114 99 110 90 85 94 127 101 99 113 80 115 85 112 112 92 97 97 91 105 84 95 108 118 118 86 89 100 (n_1 = 78) Medium Pb [Use random sample of size 6 for this level!] 78 97 107 80 90 83 101 121 108 100 110 111 97 51 94 80 101 92 100 77 108 85 (n_2 = 22) High Pb [Use random sample of size 4 for this level!] 93 100 97 79 97 71 111 99 85 99 97 111 104 93 90 107 78 95 78 86 (n_3 = 21) Remember, you must say EXACTLY how your samples are obtained!Explanation / Answer
Null Hypothesis: All the Pb have same effect.
Alternative Hypothesis: At least one Pb is different from other.
One-way ANOVA: Y versus X
Source DF SS MS F P
X 2 972 486 3.72 0.042
Error 20 2615 131
Total 22 3587
S = 11.43 R-Sq = 27.11% R-Sq(adj) = 19.82%
Conclusion : The estimated p-value of the F-statistic is 0.042. Hence we can conclude that at leat level is different from other at 0.05 level of significance.
Tukey 95% Simultaneous Confidence Intervals
All Pairwise Comparisons among Levels of X
Individual confidence level = 98.01%
X = High subtracted from:
X Lower Center Upper +---------+---------+---------+---------
Low -10.61 5.94 22.49 (----------*----------)
Mediaum -28.10 -9.42 9.27 (------------*-----------)
+---------+---------+---------+---------
-30 -15 0 15
Ll the confidence interval included zero. Hence there is no significance between High VS Low and High VS Medium.
X = Low subtracted from:
X Lower Center Upper +---------+---------+---------+---------
Mediaum -29.64 -15.36 -1.07 (---------*--------)
+---------+---------+---------+---------
-30 -15 0 15
Conclusion: The confidence interval does not include zero. Hence, Low Pb is significant from Medium Pb.
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