The circumference of a particular species of tree was thought to be different de

Question

The circumference of a particular species of tree was thought to be different depending on certain geographical factors. An SRS of 60 trees is selected in Sequoyah National Forest, where it is found that = 6 meters with a standard deviation = 3 meters. A second SRS of size 40 is independently selected in Yellowstone National Forest, and it is found that = 4 meters with a standard deviation = 2 meters. Let m1 and m2 represent, respectively, the true mean circumferences of this particular species of tree. Assume the two-sample t procedures are safe to use. 11. The degrees of freedom for these t procedures are closest to a. 99. b. 98. c. 60. d. 50. 12. The researcher tests the following hypotheses: H0 : m1 = m2, Ha : m1 m2 The 90% confidence interval is 2 ± 0.83 meters. Based on this confidence interval, a. we would reject the null hypothesis of no difference at the 0.10 level. b. the P-value is less than 0.10. c. neither a nor b is correct. d. both a and b are correct.

Explanation / Answer

The degrees of freedom for these t procedures are closest to Correct Answer: (b) 98.

Since n1 + n2 - 2 = 60+40 - 2 = 98

Given  The 90% confidence interval is 2 ± 0.83 meters (1.17,2.83)

Based on this confidence interval, 0 is not in the above interval.

So we reject H0.

P-Value: 0.0004

Here P-value < alpha 0.10, so we reject H0

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