MS 150 Statistics spring 2007 quiz 6 • Name:

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.

1. __________ Determine the sample size n.
2. __________ Calculate x.
3. __________ Calculate the sample standard deviation sx.
4. __________ Calculate the standard error of the mean σ_x.
5. __________ What is the confidence level c?
6. __________ Calculate t-critical t_c.
7. __________ Calculate the margin of error for the mean E.
8. Write out the 95% confidence interval:
   ___________ ≤ μ ≤ ___________
9. __________ Based on the lower limit above, what is the predicted minimum amount of money that can be raised over the next 13 years?
10. __________ Based on the upper limit above, what is the predicted maximum amount of money that can be raised over the next 13 years?
11. __________ The college set an original goal of 20 million dollars in the endowment fund by 2020. In 2006 the endowment fund was 2.8 million dollars. Without regard to interest, can the college reach its original goal of 20 million by 2020 - just 13 years away?

A sample size n of 1541 8^th 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.

12. __________ Write the sample size n.
13. __________ Write down the sample success proportion p as a decimal.
14. __________ Calculate q.
15. __________ Calculate the standard error of the proportion.
16. __________ Calculate the margin of error E for the proportion.
17. Write out the 95% confidence interval:
    ___________ ≤ P ≤ ___________
18. In 2005, 11% of the 8^th grade students attained 80% correct or better - a level referred to as mastery of the material - on the National Standards Test in mathematics. The FSM education sector JEMCO report of August 2006 states that the improvement from 11% mastery to 12% mastery in 2006 (12.26%) is a significant improvement.
    1. Is the improvement statistically significant based on your confidence interval?
    2. WHY?

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