Give the correct answer and solve givena.

Question

Give the correct answer and solve given
a. Test for a difference in the means in the two populations using an $[α = .05 t - t e s t .]$
b. Place a 95% confidence interval on the difference in the means of the two populations.
c. Compare the inferences obtained from the results from the Wilcoxon rank sum test and the -test.
d. Which inferences appear to be more valid, inferences on the means or the medians?

Answer 1

$[{\overset{―}{x}}_{1} = \frac{\sum ξ}{n_{1}} = 5.0625, n_{1} = 8 (p o p A) x_{2} = \frac{\sum ξ}{n_{2}} = 4.2, n_{2} = 8 (p o p (B))$
$H_{0} : μ_{1} - μ_{2} = 0$
$H_{1} : μ_{1} - μ_{2} \neq q 0$
$8_{1} = 0.04926$
$8_{2} = 0.5757$
$S_{p} = P \infty \leq d S . D .$
$S_{p} = \sqrt{\frac{(n_{1} - 1) 8_{1}^{2} + (8_{2} - 1) s_{2}^{2}}{n_{1} + n_{2} - 2}}$
$S_{p} = \sqrt{\frac{8 (2427) + 8 (3314)}{14}}$
$S_{p} = 0.57246$
Test statistic(x) $= \frac{{\overset{―}{x}}_{1} - {\overset{―}{x}}_{2}}{S_{p} \sqrt{\frac{1}{n_{1}} + \frac{1}{n_{2}}}}$
$= \frac{5.0625 - 4.2}{0.57246 \sqrt{\frac{1}{8} + \frac{1}{8}}} = 3.01$
Critical value $= \pm Z_{\frac{0.5}{1}} = \pm Z_{\frac{- 0.5}{2}} = \pm 1.96$
Test statistic $>$ critical value $\Rightarrow$ Reject $H_{0}$
Population Means are diguficantly different
$95 %$ Confidence Interval:
$μ_{1} - μ_{2} \in ({\overset{―}{z}}_{1} - {\overset{―}{z}}_{2} \pm z_{\frac{k}{2}} \cdot S_{p} \sqrt{\frac{1}{n_{1}} + \frac{1}{n_{2}}})$
$μ_{1} - μ_{2} \in (0.8625 \pm 0.561)$
$μ_{1} - μ_{2} \in (0.3015, 1.4235)$

Give the correct answer and solve givena.

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