### MS 150 Statistics spring 2007 test two • Name:

#### Part I: Confidence interval for a mean

Palikir campus
BuildingCost \$/feet²
Classroom A0.26
Classroom B0.16
Cafeteria C0.39
Dormitory D0.19
Dormitory E0.18
Faculty F0.80
Faculty F20.67
Administration G 0.53
Library H0.52
Bookstore K0.57
Agriculture L0.55

The table provides the power cost per square foot for the buildings on the Palikir campus. Construct a 95% confidence interval for the population mean cost in dollars per square foot (feet²).

1. __________ Determine the sample size n.
2. __________ Calculate x.
3. __________ Calculate the sample standard deviation sx.
4. __________ Calculate the standard error of the mean σx.
5. __________ What is the confidence level c?
6. __________ Calculate t-critical tc.
7. __________ Calculate the margin of error for the mean E.
8. Write out the 95% confidence interval:
___________ ≤ μ ≤ ___________
9. The 95% confidence interval for the population mean cost in dollars per square foot provides guidance for cost savings at the college. Given limited budgets even for power reduction, the administration wants to spend money on conserving power first in those building where the most savings might be realized. Buildings that exceed the 95% confidence interval for the mean power cost are where the most savings are likely to be realized in a first round of energy conservation measures. What buildings have a cost per square foot that exceeds the 95% confidence interval?

#### Part II: Confidence interval for a population proportion

You will be given a penny. Using a sample size of ten flips, you will be investigating whether a population probability of 0.50 for heads is a possibility. Flip the penny ten times. Record the number of heads r. Use the number of heads/ten flips as your sample proportion p for the proportion of heads (p = r/n). Find the 95% confidence interval for the population proportion P. Use a spreadsheet to make your calculations, rounding answers to two decimal places on this test.

1. __________ Write the sample size n.
2. __________ Write the number of heads r.
3. __________ Write down the sample proportion p.
4. __________ Calculate q.
5. __________ Calculate the standard error of the proportion.
6. __________ What is the confidence level c?
7. __________ Calculate t-critical tc.
8. __________ Calculate the margin of error E for the proportion.
9. Write out the 95% confidence interval:
___________ ≤ P ≤ ___________
10. __________ Is a population proportion of P = 0.50 a possible population proportion based on your experiment?

Formulas are written for OpenOffice.org Calc. Replace semi-colons with commas for Excel.

Confidence interval statistics
Statistic or ParameterSymbolEquationsOpenOffice
Degrees of freedomdf= 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 sample mean σx =sx/SQRT(n)
Calculate the margin of error E for a mean for 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 sampler
Proportion of successes or desired result in a samplep r ÷ n=r/n
Proportion of non-successes, not the desired, or alternate result in a sample q1 − p=1-p
Standard error of a proportion p σp =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
 Building Usage/KwH Billing @ 0.34/KwH Area/feet² Amt/psf Classroom A 7417 \$2,521.78 9642 \$0.26 Classroom B 4438 \$1,508.92 9642 \$0.16 Cafeteria C 6600 \$2,244.00 5760 \$0.39 Dormitory D 5748 \$1,954.32 10280 \$0.19 Dormitory E 5460 \$1,856.40 10280 \$0.18 Faculty F 9504 \$3,231.36 4032 \$0.80 Faculty F2 9359 \$3,182.06 4752 \$0.67 Administration G 13824 \$4,700.16 8820 \$0.53 Library H 27400 \$9,316.00 17768 \$0.52 Bookstore K 4801 \$1,632.34 2880 \$0.57 Agriculture L 4403 \$1,497.02 2736 \$0.55 Info Tech M 1096 \$372.64 4800 \$0.08 Maintenance N 4591 \$1,560.94 4800 \$0.33 FSM China Cntr 6800 \$2,312.00 34478 \$0.07 Water well 4480 \$1,523.20 Monthly mean total \$39,413.14 Annual estimated total \$472,957.68