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 | |||
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Statistic or Parameter | Symbol | Equations | Excel |
Degrees of freedom | df | = n-1 | |
Find a z_{c} value from a confidence level c | z_{c} | =ABS(NORMSINV((1-c)/2)) | |
Find a t_{c} value from a confidence level c | t_{c} | =TINV(1-c,df) | |
Calculate an error tolerance E of a mean for n ³ 30 using sx | E | =z_{c}*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 | =t_{c}*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 |