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 | ||