0673chapter8 - Chapter 8 Hypothesis Testing 8-2 Basics of...

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Chapter 8 Hypothesis Testing 8-2 Basics of Hypothesis Testing 1. Given the large sample size and the fact that 20% is so much less than 50%, it is apparent that any confidence interval for the proportion of bosses that are good communicators would fall entirely below 50%. Assuming the magazine has properly interpreted the survey, the results appear to support the claim that “less than 50% of bosses are good communicators” but not necessarily that “less than 50% of the people believe that bosses are good communicators” – those are two different statements that should not be confused. Given that the responders constitute a voluntary response sample, and not a random sample, it is likely that they are not representative of the population and consist largely of people with strong feelings on and/or a personal interest in the topic. The results should not be used to support the stated claim. 2. Since the P-value gives the probability of obtaining the observed result or more extreme results by chance alone, the smallest p-value of 0.001 gives the strongest evidence for the alternative hypothesis and would be the preferred result. 3. No. Since the claim that the mean is equal to a specific value must be the null hypothesis, the only possible conclusions are to reject that claim or to fail to reject that claim. Hypothesis testing cannot be used to support a claim that a parameter is equal to a particular value. 4. No. Sample data that is not consistent with a claim cannot be used to support that claim. In particular, no sample proportion less than 0.5 can ever be used to support a claim that the population proportion is greater than 0.5. 5. If the claim were not true, and p 0.5, then getting 90 heads in a sample of 100 tosses would be an unusual event. There is sufficient evidence to support the claim. 6. If the claim were not true, and p 0.35, then getting 0.955(2480) = 2368 households with telephones in a sample of 2480 households would be an unusual event. There is sufficient evidence to support the claim. 7. If the claim were not true, and μ 75, then getting a mean pulse rate of 74.4 in a sample of students would not be an unusual event. There is not sufficient evidence to support the claim. 8. If the claim were not true, and σ 15, then getting a standard deviation of 14.8 in a sample of 40 movie patrons would be not an unusual event. There is not sufficient evidence to support the claim. 9. original claim: μ > $60,000 H o : μ = $60,000 H 1 : μ > $60,000 10. original claim: p = 0.20 H o : p = 0.20 H 1 : p 0.20
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Basics of Hypothesis Testing SECTION 8-2 229 11. original claim: σ = 0.62 °F H o : σ = 0.62 °F H 1 : σ 0.62 °F 12. original claim: p > 0.5 H o : p = 0.5 H 1 : p > 0.5 13. original claim: σ < 40 seconds H o : σ = 40 seconds H 1 : σ < 40 seconds 14. original claim: σ = 0.66 cm H o : σ = 0.66 cm H 1 : σ 0.66 cm 15. original claim: p = 0.80 H o : p = 0.80 H 1 : p 0.80 16. original claim: μ < 1 kg H o : μ = 1 kg H 1 : μ < 1 kg 17. Two-tailed test; place α /2 = 0.005 in each tail.
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0673chapter8 - Chapter 8 Hypothesis Testing 8-2 Basics of...

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