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Chapter 8: Q. 9.103 (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=10and t=-3.381

Short Answer

Expert verified

Part (a) P<0.005

Part (b) Reject H0at any significance level of 0.005or larger.

Step by step solution

01

Part (a) Step 1. Given information

The given valuesn=10,t=-3.381

02

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

Use table IV in AppendixA to estimate the P-value.
It is given that,n=10,t=-3.381and test is left tailed.
Determine the degrees of freedom using the following formula,
df=n-1=10-1=9
A t-curve is symmetric about 0 , so the area to the left of-3.381equals to the area to the right of3.381, which can estimate by using table-IV. In thedf=9row of the table-IV, we can see that the t-value3.381is greater thant0.005=3.250 .
Hence, the area under the t-curve that lies to the right of3.381is less than0.005.
Consequently, the area under the t-curve that lies to the left oft0=-3.381is also less than0.005.
Therefore, P<0.005.
03

Part (b) Step 1. Given information 

The givenn=10,t=-3.381

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 of0.005or larger.
For significance levels smaller than0.005, table-IV is not sufficiently detailed to help us to decide whether to rejectH0.

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Most popular questions from this chapter

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