Question

Twenty seven students enrolled in MAT 120.  A random sample of 5 students compared their exam scores and found the following: 60, 89, 77, 68, and 91.  Calculate a 95% confidence interval for the mean of the entire class. What is the lower bound? Round your answer to the nearest tenth.  

show the steps please. jf you any app like application like R studio or Excel. please place screenshot

Answer 1

So we need to find the 95% CI for the mean scores

I am using R studio and attaching the code as well the the output below and will explain in detail further

> x=c(60,89,77,68,91) > (mean(x)+qt(0.975,4)*(var(x)^0.5)/5^0.5) [1] 93.54258 #this is the upper bound of CI > (mean(x)-qt(0.975,4)*(var(x)^0.5)/5^0.5) [1] 60.45742 #This is the lower bound of CI

So the confidence interval is given by

Where t is the t distribution value with n-1=5-1=4 df.

s is the square root of the estimate of variance.

n is the number of sample observations.

Hence the interval is given by

(60.45742,93.54258).

I hope its clear.

Thank you !!!