A young man in his early twenties was found dead with several cans of petroleum-based cleaners and a plastic bag by his side. Investigators made the initial hypothesis that the young man had died of asphyxiation from inhaling the volatile fumes from the cleaners. The estimated time of death was 16 hours before discovery. When the autopsy was conducted several days later, only trace amounts of volatile petroleum-based compounds could be detected in his lungs, well beneath the lethal level. Is the original hypothesis of death by asphyxiation from inhalants still valid? Explain why only trace levels would be found.

Describe a confidence interval for the mean of a population by stating 1. a population and a quantitative variable on that population, 2. a sample size, 3. a sample mean of that variable, and 4. a sample standard deviation, and 5. a confidence level, then 6. finding the interval. Then perform a test of significance on the mean of the population by stating 7. both a null and an alternative hypothesis and 8. an α-level, then finding 9. the one-sample t-statistic and either 10. rejecting or failing to reject the null hypothesis. Remember that you do not need to list the values of the variable for individuals in either the sample or the population, and that the values for 2, 3, 4, 5, and 8 do not need to be calculated, only stated.

**Subject Mathematics Decision Theory**