1)Assuming that a variable is normally distributed:
a)What Z‐score separates the bottom quartile of a population from everyone else?
b)What Z‐score separates the top 18% of a population from everyone else?
c)What Z‐score separates the bottom 2.5% of a population from everyone else?
d) What proportion of the sample will have z-scores between -0.20 and 1.64?
e) What proportion of the sample will have z-scores between -0.48 and -0.08?
2) What is the relationship between standard deviation and standard error? A study of 365 randomly selected kindergarten students across the US revealed that they had seen an average of 3000 hours of television.
a) What is your best guess for the average amount of television viewing among all US kindergarteners? Explain your answer.
b) If the standard deviation in your sample is 300 hours, what is the 95% confidence interval (C.I.) of the expected mean television viewing for all kindergarteners in the US?
d)responses from part b and c to answer this question: assuming nothing else changes, what happens to the width of the confidence interval as the sample deviation increases?
4) On one gloomy weekend, with nothing else to do, McRee hosts a campus contest to see who can listen to the 80’s song by Barnes & Barnes titled “Fish Heads” the most number of times in a row without collapsing in agony. (Listen if you dare.) One hundred students from the student body are selected at random to participate. Upon reviewing the data, Dr. McRee discovers that that the mean number of song plays before a student collapsed in agony was 85 song plays, and the standard deviation was 9 song plays. Please answer the following questions about the probable resilience of the UP student body:
a) What is your best guess for the average amount of times UP students could endure this song? Explain your answer.
b) How many times could a randomly selected UP student listen to Fish Heads without collapsing, to fall within the middle 95% of all students? Show your work.
c) How many times could a randomly selected UP student listen to Fish Heads without collapsing, to fall within the middle 99% of all students? Show your work.
d) What if McRee’s sample size was 600? What is your 95% CI for the UP population?
e) Take your responses from part b and d to answer this question: assuming nothing else changes, what happens to the width of the confidence interval as the sample size increases?