Consider the following competing hypotheses and accompanying sample data drawn i

Question

Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. Use Table 2. x1 251 2 252 S1 39 S2 19 a-1. Calculate the value of the test statistic under the assumption that the population variances are unknown but equal. (Negative values should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic a-2 Calculate the critical value at the 1% level of significance mínus sign. Round your answer to 3 decimal places.) Negative value should be indicated by a Critical value a-3. Do you reject the null hypothesis at the 1% level? O Yes, since the value of the test statistic is not less than the critical value. 0 No, since the value of the test statistic is less than the critical value. No, since the value of the test statistic is not less than the critical value. O Yes, since the value of the test statistic is less than the critical value.

Explanation / Answer

a-1.
Pooled standard deviation,
Sp = sqrt(((n1-1)*s1^2+(n2-1)*s2^2)/(n1+n2-2))
Sp = 30.6757

SE = Sp*sqrt(1/n1 + 1/n2) = 16.3969

Test statitistics,
t = (251 - 252)/16.3969 = -0.061

a-2.
Critical value = -2.681 (value calculated using calculator for df = 12)

a-3.
No. Since the value of the test statistic is not less than the critical value

b-1.

b-2.

critical value = -2.8214

b-3.

No. Since the value of the test statistic is not less than the critical value

x1(bar) 251.00 x2(bar) 252.00 s1 39.00 s2 19.00 n1 7 n2 7 SE = sqrt[ (s12/n1) + (s22/n2) ] (s12/n1) 217.2857 (s22/n2) 51.5714 SE 16.3969 DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] } [ (s12 / n1)2 / (n1 - 1) ] 7868.847 [ (s22 / n2)2 / (n2 - 1) ] 443.27 (s12/n1 + s22/n2)2 72284.16 DF = 9

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