A field researcher is gathering data on the trunk diameters of mature pine and s

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 the .10 level of significance, that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree?

Pine trees Spruce trees
Sample size 40 70
Mean trunk diameter (cm) 45 39
Sample variance 100 150


A. The data does not support the claim because the test value 1.29 is greater than 1.28.
B. The data supports the claim because the test value 2.78 is greater than 1.28.
C. The data supports the claim because the test value 2.78 is greater than 1.64.
D. The data does not support the claim because the test value 1.29 is less than 1.64.

Explanation / Answer

The test statistic is
Z=(45-39)/sqrt(100/40 +150/70)

=2.78

Given a=0.1, the critical value is |Z(0.1)|=1.28 (check standard normal table)

Since Z=2.78 is larger than 1.28, we reject Ho.

Answer: B. The data supports the claim because the test value 2.78 is greater than 1.28.

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