Q. 9.106 Exercises 9.101-9.106 pertain to... [FREE SOLUTION]

Chapter 8: Q. 9.106 (page 389)

Exercises 9.101-9.106 pertain to P-values for a one-mean t-test. For each exercise, do the following tasks,
a. Use Table IV in Appendix A to estimate the P-value,
b. Based on your estimate in part (a), state at which significance levels the null hypothesis can be rejected, at which significance levels it cannot be rejected, and at which significance levels it is not possible to decide:
Two-tailed test, $n = 8$ and $t = 3.725$

Short Answer

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Part (a):

$0.01 > P$

Part(b):

We can reject H₀, at any significance level of $0.01$ or larger. For significance levels smaller than $0.01$ , table-IV is not sufficiently detailed to help us to decide whether to reject H₀.

Step by step solution

Step 1. Given information is:

Two-tailed test, $n = 8$ and $t = 3.725$

Part (a) Step 1. Estimating P-value

$Because the test is two - tailed, the P - value (P) is the area under the t - curve with df = 8 - 1 = 7 that lies either to the left of the - 3.725 or to the right of 3.725 Because t - curve is symmetric about 0, so the area to the left of - 3.725 equals to the area to the right of 3.725 . In the df = 7 row of the table - IV, we can see that the t - value 3.725 is greater than any other t - value, the greatest being t_{0.005} = 3.499 . Therefore the area under the t curve that lies to the right of 3.725 is less than 0.005 . Consequently, the area under the t - curve that lies to the left of 3.725 is also less than 0.005 . Therefore the area under the t curve that lies either to the left of - 3.725 or to the right of 3.725 is less than 0.01 . Hence, 0.01 > P$

Part (b) Step 1. Calculating Significance Levels

$We can reject H_{0}, at any significance level of 0.01 or larger . For significance levels smaller than 0.01, table - IV is not sufficiently detailed to help us to decide whether to reject H_{0} .$

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Short Answer

Step by step solution

Step 1. Given information is:

Part (a) Step 1. Estimating P-value

Part (b) Step 1. Calculating Significance Levels

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