In a random sample of 340 cars... In a random sample of 340 cars driven at low a

Question

In a random sample of 340 cars... In a random sample of 340 cars driven at low altitudes, 46 of them produced more than 10g of particulate pollution per gallon of fuel consumed. In a random sample of 85 cars driven at high altitude, 21 of them produced more than 10g of particulate pollution per gallon of fuel consumed. (A) Construct a 98% confidence interval of the difference between the proportions for high-altitude and low-altitude vehicles. (B) Suppose a 95% confidence interval of within 0.10 of the difference is desired, what common sample size is required?

Explanation / Answer

n1 = 340

y1 = 46

p1 =46/340

= 23/170

s1 = sqrt(23/170 * 147/170 * 1/170)

= 0.0262

n2 = 85

y2 = 21

p2 = 21/85

s2 = sqrt( 21/85 * 64/85 * 1/85)

= 0.04678

p2-p1 = 19/170

s = sqrt(0.0262^2/170 + 0.04678^2/85)

= 0.02355

margin of error = 2.33 * 0.02355 = 0.0549

lower bound = 19/170 - 0.0549 = 0.057

upper bound = 19/170 + 0.0549 = 0.167

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