A study conducted by SSTA022 student to determine the proportion of COPE voters in Mankweng community who favor the construction of a road. If 140 of 400 voters who were selected at random favor the project and we use ô as an estimate of the actual proportion of all voters in the community who favor the project, what can we say with 99% confidence about the maximum error?
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- Suppose a researcher is interested in the effectiveness of a new drug intended to naturally increase hours of sleep for elderly patients experiencing insomnia. Suppose he collects information from a group of 64 patients and calculates a σ=.8 and a sample average of 6.4 hours of sleep. Is there sufficient evidence to reject the null hypothesis that his treatment is ineffective at increasing hours of sleep above 5 hours with 95% confidence?According to a certain government agency for a large country, the proportion of fatal traffic accidents in the country in which the driver had a positive blood alcohol concentration (BAC) is 0.33.Suppose a random sample of 109 traffic fatalities in a certain region results in 47that involved a positive BAC. Does the sample evidence suggest that the region has a higher proportion of traffic fatalities involving a positive BAC than the country at the α=0.05 level of significance?A smartphone manufacturer is so certain of its quality control that it offers a complete replacement warranty if the smartphone fails within 3 years. Based upon compiled data, the company notes that there is a 2 percent chance that its smartphone will fail during the first year, a 10 percent chance that a smartphone that survives the first year fails during the second year, and a 20 percent chance that a smartphone that survives the first two years fails during the third year. The warranty does not cover replacement smartphones after the third year. (a) Formulate the evolution of the status of the smartphone as a Markov Chain whose states include two abosrbing states that involve needing to honor the warranty or having the smartphone survive the warranty period. Construct the transition probability matrix and draw the transition probability diagram. (b) Determine the probability that: (a) the manufacturer will have to honor the warranty and (b) the manufacturer will not…
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- A sports psychologist tests a new coaching method and finds that of the 43 novice athletes who were trained under the new method, they only froze/choked when in high stakes competition 3.5% of the time. If it is known that all novice athletes tend to freeze/choke 6% of the time when in high stakes competition (with a 3.2% average variation from the mean), what would the expected rate of all novice athletes trained using the new coaching method with 92% confidence? What is the highest bound estimate for how often all novice athletes would choke if trained under the new method?What is the estimated standard error of the means (Sm1-m2)?A sports psychologist tests a new coaching method and finds that of the 43 novice athletes who were trained under the new method, they only froze/choked when in high stakes competition 3.5% of the time. If it is known that all novice athletes tend to freeze/choke 6% of the time when in high stakes competition (with a 3.2% average variation from the mean), what would the expected rate of all novice athletes trained using the new coaching method with 92% confidence? What is the lower bound estimate for how often all novice athletes would choke if trained under the new method?
- During the Covid crisis, there were lockdowns and working-from-home, which made collecting data on unemployment more challenging. Researchers from Heriot Watt University conducted a survey of 400 individuals in the labour force to assess rise in unemployment in September 2020. The object was to find out whether the unemployment rate had risen above a benchmark proportion of 6 per cent of the labour force in Malaysia. Of the surveyed persons, 34 reported being unemployed in the week prior to the survey. Conduct a two-tailed test of whether unemployment rate during this period was 6 per cent. Set out your null and alternative hypotheses, significance level, test statistic, assumptions and sampling distribution clearly. Conduct the test and comment on the economic significance of the findingsOf a random sample of 100 college students, 35 expected to achieve a higher standard of living than their parents, 43 expected a lower standard of living, and 22 expected about the same standard of living as their parents. Do these data present strong evidence that, for the population of students, more expect a lower standard of living compared with their parents than expect a higher standard of living?