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Chapter 8: Q. 9.101 (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

Right-tailed test,n=20 andt=2.235

Short Answer

Expert verified

Part (a) 0.01<P<0.025

Part (b) We can reject H0at any significance level of 0.025or larger, and can not reject H0at any significance level of 0.01or smaller.

Step by step solution

01

Part (a) Step 1. Given information

The given Right-tailed testn=20,t=2.235

02

Part (a) Step 2. Use Table IV in Appendix A to estimate the P-value 

Because the test is right tailed, the P-value (P)is the area under the t-curve with

df=20-1=19

that lies to the right of observed t value,t0=2.235 ;
i.e.P=P(t>t0), wheret~t19.
In the df=19row of the table-IV, we can see that the two t-values that straddle 2.235in between t0.025=2.093and t0.01=2.593. Therefore the area under the t-curve that lies to the right of t0=2.235is between 0.01and 0.025.
Hence,0.01<P<0.025

03

Part (b) Step 1. Given information

The given Right-tailed testn=20,t=2.235

04

Part (b) Step 2. 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 

We can rejectH0at any significance level of0.025or larger, and can not rejectH0at any significance level of0.01or smaller.
For significance levels between 0.01and 0.025, table-IV is not sufficiently detailed to help us to decide whether to rejectH0

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