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Chapter 8: Q. 9.72 (page 380)
Explain why considering outliers is important when you are conducting a one-mean z-test.
The test statistic, z may be unduly effected by outliers since the sample mean is not resistant to outliers. That is why we consider outliers when we are conducting a one-mean z-test.
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In Exercises 9鈥�12, refer to the exercise identified. Make subjective estimates to decide whether results are significantly low or significantly high, then state a conclusion about the original claim. For example, if the claim is that a coin favours heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favours heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).
Exercise 8 鈥淧ulse Rates鈥�
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.
Smoking Stopped In a program designed to help patients stop smoking, 198 patients were given sustained care, and 82.8% of them were no longer smoking after one month (based on data from 鈥淪ustained Care Intervention and Post discharge Smoking Cessation Among Hospitalized Adults,鈥� by Rigotti et al., Journal of the American Medical Association, Vol. 312, No. 7). Use a 0.01 significance level to test the claim that 80% of patients stop smoking when given sustained care. Does sustained care appear to be effective?
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?
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.
Stem Cell Survey Adults were randomly selected for a Newsweek poll. They were asked if they 鈥渇avor or oppose using federal tax dollars to fund medical research using stem cells obtained from human embryos.鈥� Of those polled, 481 were in favor, 401 were opposed, and 120 were unsure. A politician claims that people don鈥檛 really understand the stem cell issue and their responses to such questions are random responses equivalent to a coin toss. Exclude the 120 subjects who said that they were unsure, and use a 0.01 significance level to test the claim that the proportion of subjects who respond in favor is equal to 0.5. What does the result suggest about the politician鈥檚 claim?
Interpreting Power For the sample data in Example 1 鈥淎dult Sleep鈥� 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 鈥渘oncentrality parameter鈥� makes calculations of power much more complicated than the process described in Section 8-1, so software is recommended for power calculations.)
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