Assuming that you have a sample of n_1 = 8, with the sample mean X_1 = 42, and a
ID: 3160524 • Letter: A
Question
Assuming that you have a sample of n_1 = 8, with the sample mean X_1 = 42, and a sample standard deviation S_1 = 4, and you have an independent sample of n_2 = 15 from another population with a sample mean of X_2 = 34 and a sample standard deviation S_2=5, What is the value of the pooled-variance t_STAT test statistic for testing H_0: = mu_1 = mu_2? In finding the critical value, how many degrees of freedom are there? Using the level of significance a = 0.01, what is the critical value for a one-tail test of hypothesis H_0:mu_1 lessthanorequalto mu_2 against the alternative, H_1: mu_1> mu_2? What is your statistical decision? What assumptions about the two populations are necessary in Problem 1.Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u1 - u2 <= 0
Ha: u1 - u2 > 0
At level of significance = 0.01
As we can see, this is a right tailed test.
Calculating the means of each group,
X1 = 42
X2 = 34
Calculating the standard deviations of each group,
s1 = 4
s2 = 5
Thus, the pooled standard deviation is given by
S = sqrt[((n1 - 1)s1^2 + (n2 - 1)(s2^2))/(n1 + n2 - 2)]
As n1 = 8 , n2 = 15
Then
S = 4.69041576
Thus, the standard error of the difference is
Sd = S sqrt (1/n1 + 1/n2) = 2.053452378
As ud = the hypothesized difference between means = 0 , then
t = [X1 - X2 - ud]/Sd = 3.895878028 [ANSWER, pooled variance t statistic]
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b)
Getting the critical value using table/technology,
df = n1 + n2 - 2 = 21 [ANSWER]
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c)
Hence, by table/technology,
tcrit = 2.517648016 [ANSWER]
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d)
As t > 2.518, we REJECT HO. [ANSWER]
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e)
We assume that the populations are approximately normally distributed. [ANSWER]
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Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!