|Dollars per year|
The table provides the amount of money raised per year over a six year period for the endowment fund. The endowment fund is intended to help fund the college after Compact II expires in 2023. Construct a 95% confidence interval for the population mean μ money raised per year.
A sample size n of 1541 8th grade students in the FSM took the National Standards Test in mathematics administered in 2006. 189 students of the 1541 achieved 80% correct or better - a level that the FSM refers to as mastery of the material. This represents a sample success proportion p in percentage of 12.26% of the students. Find the 95% confidence interval for the population proportion P.
Formulas are written for OpenOffice.org Calc. Replace semi-colons with commas for Excel.
|Confidence interval statistics|
|Statistic or Parameter||Symbol||Equations||OpenOffice|
|Find the limit for a confidence interval for n ≥ 30 using a normal distribution with p as the area to the left of the limit||=NORMINV(p;μ;σ/SQRT(n))|
|Degrees of freedom||df||= n − 1||=COUNT(data)-1|
|Find a t-critical tc value from a confidence level c and sample size n||tc||=TINV(1-c;n-1)|
|Standard error of the mean||σx||=sx/SQRT(n)|
|Calculate the margin of error E for a mean for any n ≥ 5 using sx.||E||=tc*sx/SQRT(n)|
|Calculate a confidence interval for a population mean μ from the sample mean x and margin of error E for the mean.||x − E ≤ μ ≤ x + E|
|Number of successes or desired results in a sample||r|
|Proportion of successes or desired result in a sample||p||r ÷ n||=r/n|
|Proportion of non-successes, not the desired, or alternate result in a sample||q||1 − p||=1-p|
|Standard error of a proportion p||σx||=SQRT(p*q/n)|
|Margin of error E for a proportion p||E||=TINV(1-c;n-1)*SQRT(p*q/n)|
|Calculate a confidence interval for a population proportion P from the sample proportion p and the margin of error E for the mean.||p − E ≤ P ≤ p + E|