Question

Find the 90% confidence interval for the mean TOEFL score from 5 randomly chosen graduate school applicants. Scores were normally distributed with unknown standard deviation
-> 5 TOEFL score: 550 590 490 480 510

Answer 1

solution:

first of all calculating the mean and standard deviation from the sample data

mean =

dx is calculated as = X- mean of X

standard deviation =

significance level = = 1-0.9 = 0.10

since population standard deviation is not known, so we will use the t distribution

degree of freedom = n-1 = 5-1 = 4

critical value of t =

critical value of t is found out from the t table

margin of error =

so confidence interval for population mean =

so upper bound of interval = 524 + 43.48 = 567.48

lower bound of interval = 524 - 43.48 = 480.52

90% confidence interval for true population mean = (480.52 , 567.48)

demonstration of finding t critical value from the t table as follows: