# STAT 200 Homework 6 Assignment

| July 29, 2018

1. A stress level study based on a random sample of 60 undergraduates at your university reporteda mean of 78 (on a 0 to 100 scale) with a margin of error of 9 for 95% confidence.(a) Give the 95% confidence interval.(b) If you want 99% confidence for the same study, would you margin of error be greater than,equal to, or less than 9? Explain your answer.2. Consider the stress level study in Question 1. For a sample size of 60 we have a margin of errorof 9. But if we want to have a smaller margin of error of 3, what is the sample size we shouldhave? Show all your work.3. * For one vehicle equipped with an mpg monitor, the miles per gallon were recorded each timethe gas tank was filled, and then the monitor was reset. Here are the mpg values for a randomsample of 20 of these records: (data is attached)Suppose that the standard deviation ???? = 3.5 mpg is known.(a) What is ???? ????? , the standard deviation of ????? ?(b) Give a 95% confidence interval for ????, the mean miles per gallon for this vehicle. (The mpgvalue for this vehicle is assumed to follow a normal distribution.)(c) *R Bonus: Use R to calculate the sample standard deviation and compare to the assumedvalue of ???? = 3.5. Does the assumption appear to be reasonably accurate? Explain.4.Here are several situations where there is an incorrect application of the statistical ideas wehave been studying. In each case write a short paragraph explaining what is wrong in eachsituation and why it is wrong.(a) A random sample of size 30 is taken from a population that is assumed to have a standarddeviation of 5. The standard deviation of the sample mean is 5/30.(b) A researcher tests the following null hypothesis: ????0 : ????? = 23(c) A study with ????? = 45 reports statistical significance for ???? ???? : ???? > 50.(d) A researcher tests the hypothesis ????0 : ???? = 350 and concludes that the population mean isequal to 350.5. *A test of Null hypothesis ????0 : ???? = ????0 gives test statistic z=1.86.(a) What is p-value if the alternative hypothesis is ???? ???? : ???? > ????0 ?(b) What is p-value if the alternative hypothesis is ???? ???? : ???? < ????0 ?(c) What is p-value if the alternative hypothesis is ???? ???? : ???? ? ????0 ?(d) *R Bonus: Use R to calculate the P-values for (a)-(c) and include the code and results.

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