Q. 9.104 Exercises 9.101-9.106 pertain to... [FREE SOLUTION]

Chapter 8: Q. 9.104 (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:
Left-tailed test, $n = 30, t = - 1.572$

Short Answer

Expert verified

Part (a):

$0.05 < P < 0.10$

Part(b):

We can reject H₀, at any significance level of $0.10$ or larger, and cannot reject H₀, at any significance level of $0.05$ or smaller. For significance levels between $0.05$ and $0.10$ , table-IV is not sufficiently detailed to help us to decide whether to reject H₀.

Step by step solution

Step 1. Given information is:

Left-tailed test, $n = 30$ and $t = - 1.572$

Part (a) Step 1. Estimating P-value

$Because the test is left - tailed, the P - value (P) is the area under the t - curve with df = 30 - 1 = 29 that lies to the left of the observed t_{0} value = - 1.572 i . e . P - Value = P (t < t_{0}), where t ~ t_{29} A t - curve is symmetric about 0, so the area to the left of - 1.572 equals to the area to the right of 1.572, which we can estimate by using table - IV . In the df = 29 row of the table - IV, the two t - values that straddle 1.572 are t_{0.10} = 1.311 and t_{0.05} = 1.699 . Therefore the area under the t curve that lies to the right of 1.572 is between 0.05 and 0.10 . Consequently, the area under the t - curve that lies to the left of t_{0} = - 1.572 is also between 0.05 and 0.10 . Hence, 0.05 < P < 0.10$

Part (b) Step 1. Calculating Significance Levels

$We can reject H_{0}, at any significance level of 0.10 or larger, and can not reject H_{0}, at any significance level of 0.05 or smaller . For significance levels between 0.05 and 0.10, table - IV is not sufficiently detailed to help us to decide whether to reject H_{0} .$