A 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 that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree?

A)The data do not support the claim because the test value 0.48 is less than 1.28.
B)The data do not support the claim because the test value 0.98 is less than 1.28.
C)The data do not support the claim because the test value 0.98 is less than 1.64.
D)The data do not support the claim because the test value 0.48 is less than 1.64.

Question

A 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

that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree?

A)The data do not support the claim because the test value 0.48 is less than 1.28. 
B)The data do not support the claim because the test value 0.98 is less than 1.28. 
C)The data do not support the claim because the test value 0.98 is less than 1.64. 
D)The data do not support the claim because the test value 0.48 is less than 1.64.

Quizplus · Accepted Answer

The null hypothesis is that the average diameter of pine trees is not greater than the average diameter of spruce trees. The alternate hypothesis is that the average diameter of pine trees is greater than the average diameter of spruce trees.
We perform a two-sample t-test with unequal variances to test this hypothesis. Using a calculator or statistical software, we get a test value of 0.98 and a critical value of 1.28 for a 95% confidence level and a one-tailed test. Since the test value is less than the critical value, we fail to reject the null hypothesis. Therefore, we cannot conclude that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree.

A Field Researcher Is Gathering Data on the Trunk Diameters