Question

Problem 1: Confidence Interval for Percentage of Fs. (whats the answer for b)

The data set “STAT 250 Final Exam Scores” contains a random sample of 269 STAT 250 students’ final exam scores (maximum of 80) collected over the past two years. Answer the following questions using this data set.

1. What proportion of students in our sample earned Fs on the final exam? A letter grade of F is obtained with a score below 48 (i.e. 47 or lower). Hint: You can do this many ways, but in StatCrunch, go to Data à Row Selection à Interactive Tools. In the slider selectors box, click the variable “Scores” into the variable box. Then click compute. Use the slider to obtain the count by looking at the “# rows selected” presented in the first line of the box. Show your work (i.e. describe the method you used to obtain the number of Fs) and express this value as a proportion rounded to four decimal places.

(this answer ends up being p̂ = 61/269 = .2268)

b. Assuming there is a big population of students who have completed the final exam in STAT 250, write one sentence each to check the two other conditions of the Central Limit Theorem.

Answer 1

n=269 and p=0.2268

two other conditions of the Central Limit Theorem are Sample size n should be large enough so that

(condition1) np≥10 and nq≥10.

here np=0.2268*269=61 which is greater than 10, and  nq=n(1-p)=269*(1-0.2268)=208

and (condition2) npq=np(1-p)>10, here 269*0.2268*(1-0.2268)=47.17 , which is greater than 10