Many people believe that there are alien lifeforms that exist in places other than Earth throughout the universe. A potentially smaller subset of these people believe that alien life has visited earth, and an even smaller subset believe that aliens have abducted humans to study them.
In a survey that I just made up, 240 US adults were asked whether they had been abducted by aliens. 9 people in the sample said they had been, 231 said they had not been abducted by aliens.
Research Question: What proportion of US adults believe they have been abducted by aliens?
Part A: Describe the parameter in context.
Part B: State the value of the statistic and the symbol we use to denote it.
Part C: Check the conditions for making a confidence interval using the Normal distribution. (We will proceed regardless)
Part D: Make a 90% confidence interval for the parameter
Part E: Interpret the confidence interval in context. (leave values blank if you don’t get part D)
Turns out aliens are real and they’ve been abducting people to learn about us. They want to eat us, but are concerned that humans may contain too many microplastics.
An alien scientist abducted a random sample of 37 humans from all over the world and measured the concentration of micro-plastics in their blood. In the sample the mean micro-plastic concentration was 14 parts-per-million (ppm) with a standard deviation of 3.1 ppm.
The appropriate \(t^*\) value is one of the following:
# qt(.95, df=37) = 1.687094
# qt(.95, df=36) = 1.688298
# qt(.90, df=37) = 1.304854
# qt(.90, df=36) = 1.305514
# qt(.975, df=37) = 2.026192
# qt(.975, df=36) = 2.028094Part A: Describe the parameter the alien scientist is trying to estimate.
Part B: Are the conditions met to construct a 95% CI using a t-distribution?
Part C: State the correct value for \(t^*\) we want to use for a 95% CI to 6 decimal places.
Part D: Make a 95% CI for the parameter (show work)
Part E: Interpret this confidence interval in context. (leave values blank if you don’t get part D)