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Chapter 8: Q. 9.60 (page 370)
We have given the P-value for a hypothesis test. For each exercise determine the strength of the evidence against null hypothesis.
Given
The P-value is 0.086, which is in the range of 0.05 to 0.10.
The null hypothesis appears to have some support as a result of the conditions.
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Interpreting Power For the sample data in Example 1 “Adult Sleep” from this section, Minitab and StatCrunch show that the hypothesis test has power of 0.4943 of supporting the claim that hours of sleep when the actual population mean is 6.0 hours of sleep. Interpret this value of the power, then identify the value of and interpret that value. (For the t test in this section, a “noncentrality parameter” makes calculations of power much more complicated than the process described in Section 8-1, so software is recommended for power calculations.)
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.
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: “If the P is low, the null must go.” What does this mean?
c. Another memory trick commonly used is this: “If the P is high, the null will fly.” 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?
Testing Hypotheses. In Exercises 13–24, 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.
Got a Minute? Students of the author estimated the length of one minute without reference to a watch or clock, and the times (seconds) are listed below. Use a 0.05 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one minute?
69 81 39 65 42 21 60 63 66 48 64 70 96 91 65
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?
Adverse Reactions to Drug The drug Lipitor (atorvastatin) is used to treat high cholesterol. In a clinical trial of Lipitor, 47 of 863 treated subjects experienced headaches (based on data from Pfizer). The accompanying TI@83/84 Plus calculator display shows results from a test of the claim that fewer than 10% of treated subjects experience headaches.
A formal hypothesis test is to be conducted using the claim that the mean height of men is equal to 174.1 cm.
a. What is the null hypothesis, and how is it denoted?
b. What is the alternative hypothesis, and how is it denoted?
c. What are the possible conclusions that can be made about the null hypothesis?
d. Is it possible to conclude that “there is sufficient evidence to support the claim that the mean height of men is equal to 174.1 cm”?
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