Question

police have a hit and run case and need to identify the brand of red auto paint. the percentage of iron oxide, which gives paint its red color, was analyzed by two different methods. the mean and standard deviation of each were calculated. the results were 43.3 +/- 0.33 percent iron oxide and 43.6 +/- 0.14 percent iron oxide with five measurements each. are the two methods significantly different at the 95% confidence interval? assume that standard deviations are not significantly different.

Answer 1

We wish to find out the population mean (μ) plus/minus the margin of error by using the sample mean (x̅) and the sample standard deviation (σ) as below, i.e, μ = x̅ (margin of error).

	Method 1	Method 2
Sample Mean (x̅)	43.3	43.6
Sample Std. Dev. (σ)	0.33	0.14
Number of measurements (n)	5	5
Confidence Co-efficient (Z*)	1.96 (obtained from tables of Z values)	1.96
Margin of error (Z**σ/√n)	1.96*(0.33)/(√5) = 0.2892	1.96*(0.14)/(√5) = 0.1227
CL (μ = x̅ Z**σ/√n)	43.3 0.2892	43.6 0.1227

The lower limit of method 1 is (43.3 – 0.2892) = 43.0108 ≈ 43.01 while the upper limit is (43.3 + 0.2892) = 43.5892 ≈ 43.59.

The lower limit of method 2 is (43.6 – 0.1227) = 43.4773 ≈ 43.48 while the upper limit is (43.6 + 0.1227) = 43.7227 ≈ 43.72.

The two methods differ considerably at the 95% CL (ans); however, note that we took only 5 measurements and 5 measurements isn’t really a standard protocol for determining if there is considerable difference between the sample means.