### Statistics 2002 Spring Quiz 07

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?

Table of statistical and Excel Formulas
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