Question

Xylenes in the cab of an automobile were measured during two different trips. The concentrations were 31.4 (±30.0) μg/m3 and 52.0 (±29.8) μg/m3. Do these results differ at the 95% confidence level?

Can you please include the work? I do not understand where to start this.

Answer 1

Let's denote the data for the two trips by using subscripts 1 and 2.

Data given:

m₁ = 31.4

S₁ = 30

m₂ = 52

S₂ = 29.8

Calculating the standard deviation of difference of these two data distributions:

S = (S₁² + S₂²)^0.5 = S = (30² + 29.8²)^0.5 = 42.29

Calculating test statistic:

z = (m₂-m₁)/S = (52-31.4)/42.29 = 0.487

GIven significance level, = 0.05

The critical z-score for a two-sided test at this level of significance is:

z_c = 1.96

Since z < z_c, so it lies inside the critical region and hence these results do not differ significantly at the given level of confidence.

Hope this helps !