Alright, so honestly, I've actually looked up in both my textbooks as well as online tutorials for simplified explanations as to how I can solve the problems below but I still don't understand. They just spew out formulas that make no sense to me. Can someone please break it down in a simple fashion/easy terminology? TIA!
1) A student applied to a law school that has guaranteed admission if one scores at the 95th percentile or higher on the LSAT. Below that threshold, students may or may not be admitted. Assume that LSAT scores are normally distributed with a mean of 150 and a standard deviation of 10. The student scores 165. Will she be guaranteed admission to the law school on the basis of her LSAT? what is her percentile score? Her friend scored 10 lower on the percentile scale. What was her friend's LSAT score?
2) You have a dataset containing a random sample of 529 respondents and the following confidence interval for the sample of 529 respondents: 95% confidence interval for ideology: [74, 78]
a) Given the information above, what are the sample mean, the sample standard deviation, and the standard error of the mean for the ideology variable?
b) Given the same data, what is the 80% confidence interval for the mean of ideology.
(For this problem, I know that somehow you need to work backwards.. but backwards from where???)
3) You need to evaluate the procedures for flagging suspicious passengers used by the TSA. Assume that 1 in 10,000 passengers is a terrorist. If you had an algorithm that identified terrorists as terrorists 97.5% of the time and had a false positive rate of 4%, what is the probability that a passenger with a positive test is truly a terrorist?
4) You have 10 observations of a variable: 120, 112, 83, 74, 95, 125, 88, 90, 102, 103.
a) Why does the standard deviation change if you want to add one observation to the data that will not change the mean?
b) If you wanted to increase the standard deviation in the data by adding an observation, roughly where should you add the observation? Why?
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