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Chapter 8: Q. 15 (page 392)

State the decision criterion for a hypothesis test, using the P- value.

Short Answer

Expert verified

The decision criterion for the hypothesis test using the P-value is given below,

  • We can reject our null hypothesis, if the P-value is less than or equal to the level of significance.
  • We can also fail to reject our null hypothesis, if the P-value is greater than or equal to the level of significance.

Step by step solution

01

Step 1. Given information

We have to write the decision criterion for a hypothesis test using theP-value.

02

Step 2. Explanation for the answer:

There is a decision criterion for a hypothesis test, using theP-value which is given as below,

  • We can reject our null hypothesis, if the P-value is less than or equal to the level of significance.
  • We can also fail to reject our null hypothesis, if the P- value is greater than or equal to the level of significance.
  • Also the evidence against H0provided by the data will be stronger, if the P- value is smaller.

In simple, we can say that, we can rejectH0, if theP-value≤α.Otherwise, we cannot rejectH0.

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Most popular questions from this chapter

Testing Claims About Proportions. In Exercises 9–32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.

OxyContin The drug OxyContin (oxycodone) is used to treat pain, but it is dangerous because it is addictive and can be lethal. In clinical trials, 227 subjects were treated with OxyContin and 52 of them developed nausea (based on data from Purdue Pharma L.P.). Use a 0.05 significance level to test the claim that more than 20% of OxyContin users develop nausea. Does the rate of nausea appear to be too high?

Type I and Type II Errors. In Exercises 29–32, provide statements that identify the type I error and the type II error that correspond to the given claim. (Although conclusions are usually expressed in verbal form, the answers here can be expressed with statements that include symbolic expressions such as p = 0.1.).

The proportion of people who write with their left hand is equal to 0.1.

Finding P-values. In Exercises 5–8, either use technology to find the P-value or use Table A-3 to find a range of values for the P-value.

Airport Data Speeds: The claim that for Verizon data speeds at airports, the mean. The sample size is and the test statistic is

t =-1.625 .

Finding P-values. In Exercises 5–8, either use technology to find the P-value or use Table A-3 to find a range of values for the P-value Body Temperatures The claim is that for 12 am body temperatures, the mean is μ<98.6°F.The sample size is n = 4 and the test statistic is t = -2.503.

Final Conclusions. In Exercises 25–28, use a significance level of = 0.05 and use the given information for the following:

a. State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.)

b. Without using technical terms or symbols, state a final conclusion that addresses the original claim.

Original claim: Fewer than 90% of adults have a cell phone. The hypothesis test results in a P-value of 0.0003.
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