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e. What is the value of the observed test statistic, t, associated with the hypothesis test?

e. What is the value of the observed test statistic, t, associated with the hypothesis test?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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1. A study compared the number of tree species in unlogged forest plots to similar plots logged 8 years earlier. Independent random samples of both logged and unlogged plots were analyzed and the number of tree species was recorded. Tables 1 and 2 present the Shapiro-Wilk normality test for both types of forest plots and the Independent Samples t-test results. Use the information presented in these tables to answer the questions. Table 1: Tests of Normality Tests of Normality Kolmogorov-Smirnov Shapiro-Wilk Forest Plot Statistic df Sig. Statistic df Sig. Tree_Species Logged .181 12 .200 .936 12 .444 Unlogged .110 14 .200 .945 14 .480 *. This is a lower bound of the true significance. a. Lilliefors Significance Correction Table 2: Independent Samples Test Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means 95% Confidence Interval of the Difference Mean Std. Error F Sig. t df Sig. (2-tailed) Difference Difference Lower Upper Equal variances assumed Tree_Species 2.751 .110 -2.627 24 .015 -3.01190 1.14651 -5.37818 -.64563 Equal variances not assumed -2.697 23.271 .013 -3.01190 1.11661 -5.32030 -.70351 We want to test, at the 1% level of significance, whether the mean number of species in a logged forest plot is different to that found in an unlogged forest plot. To perform this test, we assume that the population standard deviations of logged and unlogged forest plots are equal.
Transcribed Image Text:1. A study compared the number of tree species in unlogged forest plots to similar plots logged 8 years earlier. Independent random samples of both logged and unlogged plots were analyzed and the number of tree species was recorded. Tables 1 and 2 present the Shapiro-Wilk normality test for both types of forest plots and the Independent Samples t-test results. Use the information presented in these tables to answer the questions. Table 1: Tests of Normality Tests of Normality Kolmogorov-Smirnov Shapiro-Wilk Forest Plot Statistic df Sig. Statistic df Sig. Tree_Species Logged .181 12 .200 .936 12 .444 Unlogged .110 14 .200 .945 14 .480 *. This is a lower bound of the true significance. a. Lilliefors Significance Correction Table 2: Independent Samples Test Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means 95% Confidence Interval of the Difference Mean Std. Error F Sig. t df Sig. (2-tailed) Difference Difference Lower Upper Equal variances assumed Tree_Species 2.751 .110 -2.627 24 .015 -3.01190 1.14651 -5.37818 -.64563 Equal variances not assumed -2.697 23.271 .013 -3.01190 1.11661 -5.32030 -.70351 We want to test, at the 1% level of significance, whether the mean number of species in a logged forest plot is different to that found in an unlogged forest plot. To perform this test, we assume that the population standard deviations of logged and unlogged forest plots are equal.
e. What is the value of the observed test statistic, t, associated with the hypothesis test? 0.013 -2.627 -2.697 O 0.015
Transcribed Image Text:e. What is the value of the observed test statistic, t, associated with the hypothesis test? 0.013 -2.627 -2.697 O 0.015
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