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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

In Exercises 9–12, refer to the exercise identified. Make subjective estimates to decide whether results are significantly low or significantly high, then state a conclusion about the original claim. For example, if the claim is that a coin favours heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favours heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).

Exercise 6 “Cell Phone”

Using Technology. In Exercises 5–8, identify the indicated values or interpret the given display. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section. Use = 0.05 significance level and answer the following:

a. Is the test two-tailed, left-tailed, or right-tailed?

b. What is the test statistic?

c. What is the P-value?

d. What is the null hypothesis, and what do you conclude about it?

e. What is the final conclusion?

Biometric Security In a USA Today survey of 510 people, 53% said that we should replace passwords with biometric security, such as fingerprints. The accompanying Statdisk display results from a test of the claim that half of us say that we should replace passwords with biometric security.

Critical Values. In Exercises 21–24, refer to the information in the given exercise and do the following.

a. Find the critical value(s).

b. Using a significance level of = 0.05, should we reject H0or should we fail to reject H0?

Exercise 17

In Exercises 9–12, refer to the exercise identified. Make subjective estimates to decide whether results are significantly low or significantly high, then state a conclusion about the original claim. For example, if the claim is that a coin favours heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favours heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).

Exercise 5 “Online Data”

In Exercises 1–4, use these results from a USA Today survey in which 510 people chose to respond to this question that was posted on the USA Today website: “Should Americans replace passwords with biometric security (fingerprints, etc)?” Among the respondents, 53% said “yes.” We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security.

Equivalence of Methods If we use the same significance level to conduct the hypothesis test using the P-value method, the critical value method, and a confidence interval, which method is not equivalent to the other two?
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