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Chapter 8: Q. 14 (page 392)
True or false: A - value of provides more evidence against the null hypothesis than a - value of . Explain your answer
The given statement is true.
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Vitamin C and Aspirin A bottle contains a label stating that it contains Spring Valley pills with 500 mg of vitamin C, and another bottle contains a label stating that it contains Bayer pills with 325 mg of aspirin. When testing claims about the mean contents of the pills, which would have more serious implications: rejection of the Spring Valley vitamin C claim or rejection of the Bayer aspirin claim? Is it wise to use the same significance level for hypothesis tests about the mean amount of vitamin C and the mean amount of aspirin?
Test Statistics. In Exercises 13鈥�16, refer to the exercise identified and find the value of the test statistic. (Refer to Table 8-2 on page 362 to select the correct expression for evaluating the test statistic.)
16. Exercise 8 鈥淧ulse Rates鈥�
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 鈥淐alculating Power鈥漣n 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?
Critical Values. In Exercises 21鈥�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 or should we fail to reject ?
Exercise 18
Testing Claims About Proportions. In Exercises 9鈥�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.
Touch Therapy Repeat the preceding exercise using a 0.01 significance level. Does the conclusion change?
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