Answer
No, see explanations.
Work Step by Step
From the data, we have $n1=6, \bar X1=150.83, s1=173.14$ and $n2=3, \bar X2=254, s2=183.47$
a. State the hypotheses and identify the claim.
$H_o: \mu1=\mu2$
$H_a: \mu1\ne \mu2$ (claim, two tail test)
b. Find the critical value(s).
$\alpha/2=0.05, df=2$
c. Compute the test value.
$t=\frac{150.83-254.0-0}{\sqrt {\frac{a73.14^2}{6}+\frac{183.47^2}{3}}}=-0.81, P=0.25$
d. Make the decision.
Since $P\gt 0.05$ we do not reject the null hypothesis.
e. Summarize the results.
At α= 0.10, it can not be concluded that there is a difference in the averages.
The result would be of concern to a cafeteria manager because the two seemingly
very different averages may not be so different when the number of samples are small.
