a. Explanation Given info: The data represents the estimate of β 2 as 0.47 and the estimated standard error of β 2 as0.15 for n = 25 data points. Calculation: State the hypothesis. Null hypothesis : H 0 : β 2 = 0 Alternative hypothesis : H a : β 2 ≠ 0 The test statistic is, t = β ^ 2 s β ^ 2 = 0.47 0.15 = 3.133 The degrees of freedom is, n − ( k + 1 ) = 25 − ( 2 + 1 ) = 22 Critical value: The rejection region requires α = 0 b. To determine To test: Whether the quadratic curve opens upward or not using t -test at α = 0.05 .

Statistics Plus New MyLab Statistics with Pearson eText -- Access Card Package (13th Edition)

13th Edition

ISBN: 9780134090436

Author: James T. McClave, Terry T Sincich

Publisher: PEARSON

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Chapter 12.6, Problem 12.50LM

To determine

To test: The significance of parameter β2 at α=0.05 .

To determine

To test: Whether the quadratic curve opens upward or not using t-test at α=0.05 .

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Chapter 12.6, Problem 12.49LM

Chapter 12.6, Problem 12.51LM

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Statistics Plus New MyLab Statistics with Pearson eText -- Access Card Package (13th Edition)

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To test: The significance of parameter β 2 at α = 0.05 .

Solution Summary: The author states the null hypothesis, stating that the test value is 3.133 and the critical value, 2.074.