1. Refer to the problem below and apply the Kruskal-wallis test to determine if
ID: 3332897 • Letter: 1
Question
1. Refer to the problem below and apply the Kruskal-wallis test to determine if there is a difference in the distributions of opinions across the four geographical regions (A, B, C, and D).
A large laboratory has four types of devices used to determine the pH of soil samples. The laboratory wants to determine whether there are differences in the average readings given by these devices. The lab uses 24 soil samples having known pH in the study, and randomly assigns six of the samples to each device. The soil samples are tested and the response recorded is the difference between the pH reading of the device and the known pH of the soil These values, along with summary statistics, are given in the following table Sample Device 307 .176 .137 042 294 .125 063 .690 079 013 240 201 019 082 050 .166 136 091 .318 .219 a. Based on your intuition, is there evidence to indicate any difference among the mean differences in pH readings for the four devices? b. Run an analysis of variance to confirm or reject your conclusion of part (a). Use a = .05Explanation / Answer
a. Based on my intuition, there is evidence to indicate that there is any difference among the mean difference in pH reading for given four devices. As we see In device D all results are positive except one and in device A, 3 of the results are negative. SO, we can see that there may be any difference between these 4 device.
b. Analaysis of Variance at alpha = 0.05
SO here F value = 16.45 > Fcr
so, we shall reject the null hypothesis and can say that there is difference in means.
SUMMARY Groups Count Sum Average Variance 5 15 3 2.5 A 5 -0.639 -0.1278 0.03103 B 5 0.109 0.0218 0.01485 C 5 0.582 0.1164 0.029054 D 5 1.234 0.2468 0.072308 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 34.84698 4 8.711746 16.45439 4.1E-06 2.866081 Within Groups 10.58897 20 0.529448 Total 45.43595 24Related Questions
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