My Question is Question #1 Parts A,B,C,D,E,F,G,H,&I. I have no examples in my notes and am wondering if you can provide the steps so that I can understand it. I've attached screenshots of the question and data provided
e Cou X e Cha X & http x | http x http x http x 3 1In x STA X e STA X @ STA X STA X Pag X + X -> C A eclass.srv.ualberta.ca/pluginfile.php/7657221/mod_resource/content/2/STAT%20252-2021%20Fall-HW2-Questions.pdf Q To S STAT 252-2021 Fall-HW2-Questions.pdf 2 / 6 - 75% + . . Statistics 252 - Homework # 2 Questions - Fall 2021 Table 1: Summary statistics for energy consumption in the six regions. Descriptives Energy consumption Std. Std. 95% Confidence Interval for Mean Mean Deviation Error Lower Bound Upper Bound Northwest 12.929 1.5392 5818 11.505 14.352 Midwest 12.071 4268 5393 10.752 13.391 Southwest 7 11.000 1.6330 6172 9.490 12.510 Northeast 7 14.286 1.8676 7059 12.558 16.013 Mideast 7 9.143 1.3452 5084 7.899 10.387 Southeast 7 9.143 1.5736 5948 7.688 10.598 Total 42 11.429 2.4158 .3728 10.676 12.181 Table 2: The overall ANOVA table for comparison of energy consumption between the six regions. ANOVA Energy consumption Sum of Squares df Mean Square sig. Between Groups 150.214 Within Groups 89.071 Total 239.286 LO 9M 314 () ENG 5:16 PMe Cou X e Cha X & http x & http x http x http x 3 1In x STA X e STA X @ STA X STA X Pag X + X -> C A eclass.srv.ualberta.ca/pluginfile.php/7657221/mod_resource/content/2/STAT%20252-2021%20Fall-HW2-Questions.pdf Q To S STAT 252-2021 Fall-HW2-Questions.pdf 3 / 6 - 75% + . . Table 3: The results of Tukey multiple comparisons for pairwise difference in mean energy consumption between regions. Multiple Comparisons Dependent Variable: Energy Tukey HSD Mean Difference 90% Confidence Interval (1) Index1 (J) Index1 ( 1-J) Std. Error Sig Lower Bound Upper Bound NW MW 8571 8408 908 1.413 3.127 SW 1.9286 8408 223 -.342 .199 NE 1.3571 8408 595 3.627 913 ME 3.7857 .8408 .001 1.515 6.056 ISE 3.7857' 8408 .001 1.515 5.056 MW NW .8571 8408 .908 3.127 1.413 SW 1.0714 8408 797 1.199 3.342 NE 2.2143 8408 115 -4.485 -056 ME 2.9286 .8408 .015 658 5.199 SE 2.9286 8408 015 .658 5.199 I SW NW 1.928 .8408 223 4.199 .342 MW -1.0714 .8408 797 3.342 1.199 NE 3.2857 8408 005 5.556 1.015 ME 1.8571 8408 259 .413 4.127 SE 1.8571 8408 259 413 4.127 NE NW 1.3571 8408 595 .913 3.627 MW 2.2143 8408 115 .056 4.485 SW 3.2857 .8408 .005 1.015 .556 ME 5.142 .8408 .000 2.873 7.413 SE 5.1429' .8408 000 2.873 7.413 ME NW 3.7857 8408 001 6.056 1.515 MW 2.9286 8408 015 5.199 658 SW -1.8571 .8408 259 4.127 413 NE 5.1429 8408 .000 -7.413 2.873 SE .0000 .8408 1.000 -2.270 .270 SE NW 3.7857' .8408 001 6.056 1.515 MW 2.9286' .8408 015 -5.199 .658 SW 1.8571 8408 259 4.127 413 NE 5.1429 8408 .000 7.413 2.873 .0000 .8408 1.000 -2.270 2.270 ". The mean difference is significant at the 0.10 level. 3 LO 9 M 31 4 CE O K () ENG 5:17 PM Ee Cou X e Cha X & http x | http x http x http x 1In x e STA X e STA X @ STA X STA X Pag X + X -> C A eclass.srv.ualberta.ca/pluginfile.php/7657221/mod_resource/content/2/STAT%20252-2021%20Fall-HW2-Questions.pdf To S STAT 252-2021 Fall-HW2-Questions.pdf 4/ 6 75% + . . Statistics 252 - Homework # 2 Questions - Fall 2021 (a) (5 marks) At the 1% significance level, carry out the most appropriate test to determine if there are any significant difference in mean energy consumption among the six regions. SHOW ALL STEPS. (b) (1 mark) What is the best estimate for the common or pooled standard deviation of the 6 populations? (c) (4 marks) Based on the SPSS output for Tukey's multiple comparisons performed at the 90% confidence level (Table 3), firstly, construct a means comparisons diagram and, secondly, summarize the results in words. (d) (10 marks) At the 97% confidence level, perform the Bonferroni method of multiple comparisons to determine which pairs of regions have different mean energy consumption. SHOW ALL STEPS, including compilation of the results in a matrix and giving the conclusion both in a means comparisons diagram and in words. Note: You only have to calculate the margin of error once since sample sizes are equal for all groups. (e) (3 marks) Compare the means comparisons diagrams you constructed in parts (c) and (d). Do they show the same results? If they show different results, explain the reasons for the difference. If they show the same results, state whether they must show the same results, or whether they could have shown different results, explaining the reasons for potential differences. (f) (8 marks): Develop a linear combination (contrast) to test the hypothesis that there is a difference in energy consumption between the Northwest and Midwest regions (combined) in comparison with the Northeast and Mideast regions (combined). Then, test this contrast at the 1% significance level. SHOW ALL STEPS of the hypothesis test (g) (8 marks) Develop a linear combination (contrast) to test the hypothesis that there is a difference in energy consumption between the Northwest region and the combined Eastern regions (i.e., Northeast, Mideast, and Southeast combined). Then, test this contrast at the 1% significance level. SHOW ALL STEPS of the hypothesis test. LO 9M 314 () ENG 5:17 PM Ee Cou X e Cha X & http x | http x http x http x 3 1In x STA X e STA X @ STA X STA X Pag X + X -> C A eclass.srv.ualberta.ca/pluginfile.php/7657221/mod_resource/content/2/STAT%20252-2021%20Fall-HW2-Questions.pdf To S STAT 252-2021 Fall-HW2-Questions.pdf 5 / 6 75% + . . (h) (6 marks) At the 5% significance level, perform the most appropriate test, SHOWING ALL STEPS, to determine whether there is a difference in energy consumption between the Western regions (NW, MW, and SW) and the Eastern regions (NE, ME, and SE), after accounting for the effect of latitude (i.e., Northern, Middle, and Southern). For this test, make use of the parameters defined at the start of Question 1. You may consider using any of the SPSS output shown in Tables 2, 4, or 5 below. [Table 2, from page 2, is repeated here below for your convenience.] Table 2: The overall ANOVA table for comparison of energy consumption between the six regions. ANOVA Energy consumption Sum of Squares df Mean Square Sig. Between Groups 150.214 Within Groups 89.071 Total 239.286 Table 4: ANOVA table for comparison of energy consumption between Western regions and Eastern regions (ignoring latitude, i.e., Northern, Middle, and Southern). ANOVA Hours Sum of Squares Mean Square Sig. Between Groups 13.714 2.431919 .1268 Within Groups 225.571 Total 39.286 Table 5: ANOVA table for comparison of energy consumption between different latitudes (Northern, Middle, and Southern) (ignoring longitude, i.e., Western versus Eastern). ANOVA Hours Sum of Squares Mean Square Sig. Between Groups 101.679 14.40864 0.000 Within Groups 137.607 Total 239.286 (i) (2 marks) Suppose a pooled t-test was performed to test for the difference in mean energy consumption between the Western regions (NW, MW, and SW) and the Eastern regions (NE, ME, and SE). What would be the of, the t-statistic and the exact P-value? You may use any of the information in the previous parts of this question to determine your answer. LO 9 M 31 4 () ENG 5:17 PM E
