The quality of the picture on a home satellite TV depends on the strength of the
ID: 3134962 • Letter: T
Question
The quality of the picture on a home satellite TV depends on the strength of the signal. Professional installation is often necessary to properly align a dish and tune in a satellite. A study was conducted to determine whether the signal strength was related to the satellite company and/or the geographic region. For each company and region, a random sample of satellite TV users was obtained, and the signal strength of each system was measured (in dBmV). The data are given in the table below.
Northeast
Southeast
Midwest
West
Company A
65.9 73.9
70.9 74.9
64.0 61.4
55.0 52.1
55.9 64.2
67.2 74.3
54.7 69.9
62.2 65.5
Company B
71.3 76.8
71.4 65.2
64.3 64.0
61.3 68.2
69.4 68.6
61.2 64.9
65.6 67.8
55.2 66.0
Company C
64.0 64.2
76.7 65.1
60.8 62.9
57.0 69.6
58.3 64.4
69.3 73.1
62.4 62.9
64.5 71.3
Analyze the data using a=.05. Perform multiple comparisons if necessary.
Northeast
Southeast
Midwest
West
Company A
65.9 73.9
70.9 74.9
64.0 61.4
55.0 52.1
55.9 64.2
67.2 74.3
54.7 69.9
62.2 65.5
Company B
71.3 76.8
71.4 65.2
64.3 64.0
61.3 68.2
69.4 68.6
61.2 64.9
65.6 67.8
55.2 66.0
Company C
64.0 64.2
76.7 65.1
60.8 62.9
57.0 69.6
58.3 64.4
69.3 73.1
62.4 62.9
64.5 71.3
Explanation / Answer
The Two-way Analysis of variance (ANOVA) is as follows
Anova: Two-Factor With Replication SUMMARY North East South East Mid West West Total Company A Count 4 4 4 4 16 Sum 285.6 232.5 261.6 252.3 1032 Average 71.4 58.125 65.4 63.075 64.5 Variance 16.33333333 30.43583333 58.04666667 41.1225 53.47866667 Company B Count 4 4 4 4 16 Sum 284.7 257.8 264.1 254.6 1061.2 Average 71.175 64.45 66.025 63.65 66.325 Variance 22.46916667 8.07 14.18916667 32.65 24.618 Company C Count 4 4 4 4 16 Sum 270 250.3 265.1 261.1 1046.5 Average 67.5 62.575 66.275 65.275 65.40625 Variance 37.84666667 27.89583333 40.94916667 16.93583333 28.23795833 Total Count 12 12 12 12 Sum 840.3 740.6 790.8 768 Average 70.025 61.71666667 65.9 64 Variance 24.39113636 25.78515152 31.01636364 25.68545455 ANOVA Source of Variation SS df MS F P-value F crit Sample 26.64541667 2 13.32270833 0.46080181 0.634446512 3.259446 Columns 446.005625 3 148.6685417 5.142102596 0.004615665 2.866266 Interaction 108.18125 6 18.03020833 0.623623398 0.710133814 2.363751 Within 1040.8325 36 28.91201389 Total 1621.664792 47Related Questions
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