An experimenter is convinced that her measuring instrument had a variability measured by variance σ2 = 4. During an experiement she recorded the measurements 4.1, 5.2, and 10.2. What is the value of the test statistic to test the hypotheses H0 : σ2 = 4 vs H1 : σ2 6= 4
A. 3.212
B. 5.285
C. 4.111
D. 8.34
Here given values are
n=3
sigma^2 =4
values=4.1,5.2,10.2
mean =(4.1+5.2+10.2)/3=19.5/3=6.5
sample variance = s^2 =(1/2)*(((4.1-6.5)^2)+((5.2-6.5)^2)+(10.2-6.5)^2) =21.14/2 =10.57
then here we use chisquare test, the test statistic is given by
chi square value =((n-1)*(s^2))/(sigma^2)
= ((3-1)*10.57)/4 = 21.14 / 4 =5.285
so option B
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