Temperatures on four different floors in a building were recorded in order to as

Question

Temperatures on four different floors in a building were recorded in order to assess whether or not the thermostats were performing consistently across floors. On each floor, temperature samples were taken at six different locations (image attached). Please do not use any statistical software for this problem. Construct an ANOVA table. Show all your calculations.You may give a range for the p-value. Can you conclude that the temperatures are different across the four floors?

Floor 1 Floor 2 |Floor 3 Floor 4 71.06 71.74 67.71 65.02 63.1 69.6 72.22 66.75 4 70.43 70.87 65.96 73.32 68.78 68.5 66.68 64.38 6 62.28 66.64 74.24 63.78 71 65.74 68.77 74.58 65.08

Explanation / Answer

H0: There is no difference between means of four floors

H1:There is a difference between means of four floors

alpha:5%

Test statistic:

From Excel

F cal=1.849

Conclusion:

P value=0.1708

Since P > 0.05, we do not reject the H0. Hence Claim is not significant.

Anova: Single Factor SUMMARY Groups Count Sum Average Variance floor1 6 401.39 66.89833 14.08618 floor2 6 416.12 69.35333 3.297587 floor3 6 421.39 70.23167 15.2297 floor4 6 398.33 66.38833 12.51994 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 62.59821 3 20.86607 1.84928 0.170786 3.098391 Within Groups 225.667 20 11.28335 Total 288.2652 23

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