In the Spring of 2001 Save Your Ear High School (SYEHS) had a population mean TOEFL score of µ = 548.
In the Spring of 2002 Save Your Ear High School had a sample size of n = 25 students take the TOEFL test. The twenty-five students had a sample mean TOEFL score of x = 536 with a standard deviation sx = 44. Construct a 95% confidence interval for the population mean TOEFL score µ for SYEHS.
Is the decline in the mean TOEFL score from 2001 to 2002 statistically significant?
|Confidence interval statistics|
|Statistic or Parameter||Symbol||Equations||Excel|
|Degrees of freedom||df||= n-1|
|Find a zc value from a confidence level c||zc||=ABS(NORMSINV((1-c)/2))|
|Find a tc value from a confidence level c||tc||=TINV(1-c,df)|
|Calculate an error tolerance E of a mean for n ³ 30 using sx||E||=zc*sx/SQRT(n)|
|Calculate an error tolerance E of a mean for n < 30 using sx. Can also be used for n ³ 30.||E||=tc*sx/SQRT(n)|
|Calculate a confidence interval for a population mean µ from a sample mean x and an error tolerance E||x - E< µ <x + E|