6. 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.
a. Identify the actual number of respondents who answered yes.
b. Identify the sample proportion and the symbol used to represent it.
c. Null and Alternative Hypotheses: Identify the null hypothesis and alternative hypothesis.
7. Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical values, then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation to the binomial distribution.
a. The drug Eliquis (apixaban) is used to help prevent blood clots in certain patients. In clinical trials, among 5924 patients treated with Eliquis, 153 developed the adverse reaction of nausea based on data from Bristol-Myers Squibb Co. Use a 0.05 significance level to test the claim that 3% of Eliquis users develop nausea. Does nausea appear to be a problematic adverse reaction?
b. The company Drug Test Success provides a 1-Panel-THC test for marijuana usage. Among 300 tested subjects, results from 27 subjects were wrong, either a false positive or a false negative. Use a 0.05 significance level to test the claim that less than 10% of the test results are wrong. Does the test appear to be good for most purposes?
8. Assume that a simple random sample has been selected and test the given claim. 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 values, and state the final conclusion that addresses the original claim.
a. 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 Cognitive Behavioral Therapy vs Zopiclone for Treatment of Chronic Primary Insomnia in Older Adults by Sivertsen et al., Journal of the American Medical Association, Vol. 295, No. 24). Assume that the sample with zopiclone subjects have a mean wake time of less than 102.8 min. Does zopiclone appear to be effective?
b. A New York Times article noted that the mean life span for 35 male symphony conductors was 73.4 years, in contrast to the mean of 69.5 years for males in the general population. Assuming that the 35 males have life spans with a standard deviation of 8.7 years, use a 0.05 significance level to test the claim that male symphony conductors have a mean life span that is greater than 69.5 years. Does it appear that male symphony conductors live longer than males from the general population? Why doesn't the experience of being a male symphony conductor cause men to live longer?
