Let X equal the weight in grams of a Low-Fat Strawberry Kudo and Y the weight of
ID: 3218524 • Letter: L
Question
Let X equal the weight in grams of a Low-Fat Strawberry Kudo and Y the weight of a Low-Fat Blueberry Kudo. Assume that the distributions of X and Y are N(mu x, sigma^2 x) and N (mu _Y, sigma^2 _Y), respectively. Let 21.7 21.0 21.2 20.7 20.4 21.9 20.2 21.6 20.6 be n = 9 observations of X, and let 21.5 20.5 20.3 21.6 21.7 21.3 23.0 21.3 18.9 20.0 20.4 20.8 20.3 be m = 13 observations of Y. Test the null hypothesis H_0:mu_x = mu _y against a two-sided alternative hypothesis. Use alpha = 0.05. Assume that the variances are equal.Explanation / Answer
Here Null Hypothesis Ho : x = y
ALternative Hypothesis H1 : x y
Here we can see that variance are equal
so we will perform t- test with equal variances
xbar = 21.03 and ybar= 20.89
sx = 0.606 ; sy = 1.007
sp2 = [(n1 -1) sx2 + (n2 -1) sy2] / (n1 + n2 -2)] = [( 8*0.6062 + 12*1.0072)/ (20)] = 0.7553
sp = 0.8691
Test Statistic: t =(xbar - ybar)- (x - y)/ sp (1/n1 + 1/n2 ) = (21.03 - 20.89)/ 0.8691 (1/9 + 1/13)
= 0.14 / 0.3768 = 0.3748
T critical for two tail and for alpha = 0.05 and dF = 20
T(critical) = 2.086
so we cannot reject null hypothesis and we can conclude that there is no significant differences between strawberry kudo and blueberry kudo.
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