Question

ome Assume that you have a sample of n-5, with the sample mean X, -43, and a sample standard deviation of S, 4, and you have an independent sample of n - 8 from another population with a sample mean of X = 37 and the sample standard deviation S, - 5. Assuming the population variances are equal, at the 0.01 level of significance, is there evidence that ? Gradeboto nyponses S W W W ents unch OAH 2 Hy = 2 c. 16 R152 4. Hoillah Hi, o Mo: H>p2 Hii Contents ay Plan & Resource Find the test statistic ISTA Round to two decimal places as needed) rary scessible Resour 1 - Vi M ore Purchase Option Enter your answer in the answer box and then click Check Answer parts Clear All Final Check Type here to search
need answer to the second and third part

Answer 1

When the population variances are assumed to be equal, then the formula is:

$t = \frac{\bar X_1 - \bar X_2}{\sqrt{ \frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2}(\frac{1}{n_1}+\frac{1}{n_2}) } }$

$\rightarrow t = \frac{43 - 37}{\sqrt{ \frac{(5-1)*4^2 + (8-1)*5^2}{5+8-2}(\frac{1}{5}+\frac{1}{8}) } }$

$\rightarrow t = {\color{DarkRed} 2.26}$

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