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Question

c )-secure! htt and an air toxin ot certain region. from of g date on both Indoor 0.09 0.10 0.11 0.14 0.14 0.14 0.15 0.16 0.17 Outdoor 0.25 0.64 0.43 0.so 0.93 0.31 0.45 0.80 0.82 10 11 12 13 14 15 16 17 Indoor 0.17 0.19 0.19 0.20 0.20 0.20 0.20 0.21 Outdoor 0,24 0.28 0.28 1.51 0.62 0.25 0.17 0.98 18 19 20 21 22 23 24 25 Indoor 0.22 0.24 0.24 0.25 0.25 0.27 0.28 0.30 Outdoor 1.55 0.86 0.48 0.08 o.s0 0.84 0.45 1.20 26 27 28 29 30 31 32 33 Indoor 0.30 0.31 0.36 0.41 0.42 0.47 0.56 0.64 Outdoor 0.44 0.23 0.33 1.22 0.66 0.72 0.95 0.32 decimal places.) -0.50 × ,1419 )(nanograma/m, × we can 95% be conndent that the true average concentration of hexavalent chromiin outdoors exceeds the true average concentration indoors by an amount otside the interval.

Explanation / Answer

(a) Here it is the paired data sample test. So,

Here first the difference table

Here average difference dbar = -0.3639

Standard deviation of difference sd = 0.3868

standard error of difference sed = sd / sqrt(n) = 0.3868/ sqrt(33) = 0.06733

Here 95% confidence interval for mean difference = dbar +- tdf,0.05 sed

= - 0.3639 +- 2.036933 * 0.06733

= (-0.5011, -0.2268) = (-0.50, -0.23) (in two decimal places)

Here the interpretation is correct.

(c) Here if a 34th value is randomly selected from the population, predicted difference would lie in between 95% confidence interval but with using Z values.

95% confidence interval = dbar +- tdf,0.05 sd = -0.3639 + 1.96 * 0.3868

= (-1.1220 , 0.3942 ) = (-1.12, 0.39)

House Indoor Outdoor Difference 1 0.09 0.25 -0.16 2 0.1 0.64 -0.54 3 0.11 0.43 -0.32 4 0.14 0.5 -0.36 5 0.14 0.93 -0.79 6 0.14 0.31 -0.17 7 0.15 0.45 -0.3 8 0.16 0.8 -0.64 9 0.17 0.82 -0.65 10 0.17 0.24 -0.07 11 0.19 0.28 -0.09 12 0.19 0.28 -0.09 13 0.2 1.51 -1.31 14 0.2 0.62 -0.42 15 0.2 0.25 -0.05 16 0.2 0.17 0.03 17 0.21 0.98 -0.77 18 0.22 1.55 -1.33 19 0.24 0.86 -0.62 20 0.24 0.48 -0.24 21 0.25 0.08 0.17 22 0.25 0.5 -0.25 23 0.27 0.84 -0.57 24 0.28 0.45 -0.17 25 0.3 1.2 -0.9 26 0.3 0.44 -0.14 27 0.31 0.23 0.08 28 0.36 0.33 0.03 29 0.41 1.22 -0.81 30 0.42 0.66 -0.24 31 0.47 0.72 -0.25 32 0.56 0.95 -0.39 33 0.64 0.32 0.32 average -0.3639 Std. Dev. 0.3868

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