**Table At Bottom** Biological effects of magnetic fields are a matter of concer
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Question
**Table At Bottom** Biological effects of magnetic fields are a matter of concern and research. In an early study of the effects of a strong magnetic field on the development of mice (Bamothy 1964), 10 cages, each containing three 30-day-old albino female mice were subjected for a period of 12 days to a strong magnetic field. Thirty other mice housed in 10 similar cages were not placed in a magnetic field and served as controls. The following table shows the weight gains, in grams, for each of the cages. a. Perform a t-test to test whether the presence of a strong field had a significant effect on weight gain in these mice stating your null hypothesis, the confidence level to reject the null hypothesis (if relevant) and the p-value (if relevant). b. Repeat the analysis above using the non-parametric Mann Whitney Test. Field Present - 22.8,10.2, 20.8, 27, 19.2, 9, 14.2, 19.8, 14.5, 14.8 Field Absent - 23.5, 31, 19.5, 26.2, 26.5, 25.2, 24.5, 23.8, 27.8, 22
Explanation / Answer
This is a case of independent samples T test as both the samples are different from one another.we shall perform the analysis in the open source statistical package R , The complete R snippet is as follows
This is case of 2 tail t test as we are interested in the difference of weight GAIN
FP <- c(22.8,10.2, 20.8, 27, 19.2, 9, 14.2, 19.8, 14.5, 14.8)
FA <- c( 23.5, 31, 19.5, 26.2, 26.5, 25.2, 24.5, 23.8, 27.8, 22)
### perform t test
t.test(FP,FA,alternative = "two.sided",paired = FALSE)
### non paramteric test
wilcox.test(FP,FA,alternative = "two.sided")
The results are
> t.test(FP,FA,alternative = "two.sided",paired = FALSE)
Welch Two Sample t-test
data: FP and FA
t = -3.7806, df = 14.14, p-value = 0.001995 ## as the p value is less than 0.05 , hence we reject null in favor of alternate hypothesis and conclude that there is a signficant difference in the weight gains for the 2 groups
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-12.173973 -3.366027
sample estimates:
mean of x mean of y
17.23 25.00
> ### non paramteric test
> wilcox.test(FP,FA,alternative = "two.sided")
Wilcoxon rank sum test
data: FP and FA
W = 12, p-value = 0.002879 ## as the p value is less than 0.05 , hence we reject null in favor of alternate hypothesis and conclude that there is a signficant difference in the weight gains for the 2 groups , even for the non parameteric test
alternative hypothesis: true location shift is not equal to 0
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