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Chapter 8: Q. 9.33 (page 364)

Define the term non- rejection ratio.

Short Answer

Expert verified

The set of all possible values for which the null hypothesis is not rejected is called the rejection region.

Step by step solution

01

Step 1. To define

The term non-rejection ratio

02

Step 2. Definition

The set of all possible values for which the null hypothesis is not rejected is called the rejection region.

03

Step 3. Explanation using graph

The non-rejection region for two-failed test is shown below-

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Most popular questions from this chapter

Testing Hypotheses. In Exercises 13โ€“24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.

Insomnia Treatment A clinical trial was conducted to test the effectiveness of the drug zopiclone for treating insomnia in older subjects. Before treatment with zopiclone, 16 subjects had a mean wake time of 102.8 min. After treatment with zopiclone, the 16 subjects had a mean wake time of 98.9 min and a standard deviation of 42.3 min (based on data from โ€œCognitive Behavioral Therapy vs Zopiclone for Treatment of Chronic Primary Insomnia in Older Adults,โ€ by Sivertsenet al.,Journal of the American Medical Association, Vol. 295, No. 24). Assume that the 16 sample values appear to be from a normally distributed population, and test the claim that after treatment with zopiclone, subjects have a mean wake time of less than 102.8 min. Does zopiclone appear to be effective?

Testing Claims About Proportions. In Exercises 9โ€“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.

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Critical Values. In Exercises 21โ€“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 ฮฑ= 0.05, should we reject H0or should we fail to reject H0?

Exercise 19

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

8. Tornadoes. The claim is that for the widths (yd) of tornadoes, the mean is ฮผ<140 yd. The sample size is n = 21 and the test statistic is t = -0.024.

PowerFor a hypothesis test with a specified significance level , the probability of a type I error is, whereas the probability of a type II error depends on the particular value ofpthat is used as an alternative to the null hypothesis.

a.Using an alternative hypothesis ofp< 0.4, using a sample size ofn= 50, and assumingthat the true value ofpis 0.25, find the power of the test. See Exercise 34 โ€œCalculating Powerโ€in Section 8-1. [Hint:Use the valuesp= 0.25 andpq/n= (0.25)(0.75)/50.]

b.Find the value of , the probability of making a type II error.

c.Given the conditions cited in part (a), find the power of the test. What does the power tell us about the effectiveness of the test?
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