An field researcher is gathering data on the trunk diameters of mature pine and spruce trees in a certain area. The following are the results of his random sampling. Can he conclude, at $\alpha = 0.10$, that the average trunk diameter of a pine tree is greater than the average diameter ofa spruce tree?
$\begin{array}{lcc}
\hline & \text { Pine trees } & \text { Spruce trees } \
\hline \text { Sample size } & 60 & 80 \
\text { Mean trunk diameter, cm } & 46 & 40 \
\text { Population variance } & 155 & 127
\end{array}$

A) The data does not support the conclusion that the average pine tree trunks are larger because the test value 24.54 is greater than than the critical value 1.65.
B) The data supports the conclusion that the average pine tree trunks are larger because the test value 2.94 is greater than than the critical value 1.28.
C) The data does not support the conclusion that the average pine tree trunks are larger because the test value 1.44 is greater than than the critical value 1.28.
D) The data supports the conclusion that the average pine tree trunks are larger because the test value 2.94 is greater than than the critical value 1.65.

Question

An field researcher is gathering data on the trunk diameters of mature pine and spruce trees in a certain area. The following are the results of his random sampling. Can he conclude, at $\alpha = 0.10$, that the average trunk diameter of a pine tree is greater than the average diameter ofa spruce tree?
$\begin{array}{lcc}
\hline & \text { Pine trees } & \text { Spruce trees } \
\hline \text { Sample size } & 60 & 80 \
\text { Mean trunk diameter, cm } & 46 & 40 \
\text { Population variance } & 155 & 127
\end{array}$

A) The data does not support the conclusion that the average pine tree trunks are larger because the test value 24.54 is greater than than the critical value 1.65.
B) The data supports the conclusion that the average pine tree trunks are larger because the test value 2.94 is greater than than the critical value 1.28.
C) The data does not support the conclusion that the average pine tree trunks are larger because the test value 1.44 is greater than than the critical value 1.28.
D) The data supports the conclusion that the average pine tree trunks are larger because the test value 2.94 is greater than than the critical value 1.65.

Quizplus · Accepted Answer

The correct answer is determined by conducting a hypothesis test for the difference in means. The test statistic is calculated using the formula for two independent samples, which accounts for the sample sizes, means, and variances of both groups. The calculated test value exceeds the critical value at the given significance level ($\alpha = 0.10$), indicating that the data supports the conclusion that the average trunk diameter of pine trees is greater than that of spruce trees.

An Field Researcher Is Gathering Data on the Trunk Diameters α=0.10\alpha = 0.10α=0.10

An Field Researcher Is Gathering Data on the Trunk Diameters $\alpha = 0.10$