Question

Contaminated water: In a sample of 43 water specimens taken from a construction site, 23 contained detectable levels of lead Part 1 of 3 (a) Construct a 99% confidence interval for the proportion of water specimens that contain detectable levels of lead. Round the answer to at least three decimal places. A 99% confidence interval for the proportion of water specimens that contain detectable levels of lead is 0.339 <p < 0.731 Part: 1/3 Part 2 of 3 (b) Construct a 95% confidence interval for the proportion of water specimens that contain detectable levels of lead. Round the answer to at least three decimal places. A 95% confidence interval for the proportion of water specimens that contain detectable levels of lead is P

Answer 1

Å= 23 0.5349 43 the formula - a-sided c. I is given by Zala $(1-P) < + Zala. Decore) n (@) 990% (.I for proposition of water (22=2 = 2.576 (sounce- STATKEY -image] Here 0.005 So, 0.5349 2.576(0.5349x0.4651 43 <P < 0.5349+2.576 0.5349 x 0.4651 43 = 0.339 < p < 0.731 water proportion of (b) 95% c. I for Here [Zafe - 20.025 = 1.960 (source - STATKEY - image :) ] attached So, 0.5349 1.960 * 10.5349 x 0.4651 < p < 43 0.5349x0.4651 0.5349 +1-910 X 43 그 0.386 < p < 0.684

StatKey Theoretical Distribution Normal Distribution Reset Plot Normal Distribution Left Tail Two-Tail Right Tail Mean 0.40 Standard Deviation 0 0.35 Edit Parameters 0.30 0.25 0.20 0.0050 0.990 0.0050 0.15 0.10 0.05 0.00 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 -2.576 2.576 Activate Windows

Statkey Theoretical Distribution Normal Distribution- Reset Plot Normal Distribution Left Tail Two-Tail Right Tail Mean Standard Deviation 0.40 0 1 0.35 Edit Parameters 0.30 0.25 0.20 0.025 0.950 0.025 0.15 0.10 0.05 0.00 -4.0 -3.0 -1.0 0.0 1.0 1.0 3.0 4.0 -2b -1.960 1.960 Activate Windows

The 99% and 95% C.I is constructed using the formula mentioned. The critical values are obtained from STATKEY (image attached for reference).