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Chapter 8: Q. 20 (page 392)
Assess the evidence against the null hypothesis if the value of the hypothesis test is .
The given statement is reasonable.
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Type I and Type II Errors. In Exercises 29鈥�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 adults who use the internet is greater than 0.87.
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
In Exercises 1鈥�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: 鈥淪hould Americans replace passwords with biometric security (fingerprints, etc)?鈥� Among the respondents, 53% said 鈥測es.鈥� We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security.
Requirements and Conclusions
a. Are any of the three requirements violated? Can the methods of this section be used to test the claim?
b. It was stated that we can easily remember how to interpret P-values with this: 鈥淚f the P is low, the null must go.鈥� What does this mean?
c. Another memory trick commonly used is this: 鈥淚f the P is high, the null will fly.鈥� Given that a hypothesis test never results in a conclusion of proving or supporting a null hypothesis, how is this memory trick misleading?
d. Common significance levels are 0.01 and 0.05. Why would it be unwise to use a significance level with a number like 0.0483?
Cans of coke use the data and the claim given in exercise 1 to identify the null and alternative hypothesis and the test statistic. What is the sampling distribution of the test statistic?
Testing Hypotheses. In Exercises 13鈥�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 鈥淐ognitive Behavioral Therapy vs Zopiclone for Treatment of Chronic Primary Insomnia in Older Adults,鈥� 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?
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