For my task, I was asked a series of questions that required deep statistical analysis of the information provided and discovered. I was given a copy of date from the SAT Score Roster sent to the high school by the College Board. This roster showed gender, verbal and math scores of 303 students in a recent graduating class. With that information I took a random sample of 30 by number 1 to 303 on my list and generating 30 random integers with my calculator. I did not include repeats. I used that sample for each of the questions at hand after I concluded they were representative of the population.
The first question I was asked to address was to find the true mean SAT- Math scores for students at the high school whose information I was given. I then checked my assumptions to make sure I could safely proceed with my calculations. I concluded that it was random because I took a random sample from the population, as stated in my opening. Next, I stated it was independent because my sample of 30 is less than 10% of the 303 student’s information. The last assumption I checked was to see it followed a normal model by making sure it was a large enough population. I used the central limit theorem because my population is equal to 30. After running my test, I came up with an interval of true mean SAT- Math scores as (559.02, 637.65). From this interval, I am 95% confident that the true mean SAT- Math score for this high school is between 559.02 and 637.65.
I was then asked to use my interval to compare this high schools performance to the students with a statewide mean math score of 503. Using my interval, I concluded that the scores of this high school are higher than that of the statewide average. This is because my interval does not encompass the score of 503. The low end of my interval is 56 points higher than that of the statewide average.
The third task I was asked to