Question

Concentrations of atmospheric pollutants such as carbon monoxide (CO) can be measured with a spectrophotometer. In a calibration test, 50 measurements were taken of a laboratory gas sample that is known to have a CO concentration of 70 parts per million (ppm). A measurement is considered to be satisfactory if it is within 5 ppm of the true concentration. Of the 50 measurements, 37 were satisfactory. (a) What proportion of the sample measurements were satisfactory? (b) Find a 95% confidence interval for the proportion of measurements made by this instrument that will be satisfactory? (c) Suppose it is desirable to estimate the population proportion of satisfactory measurement within ±0.03, how big a sample of measurements should be? (d) Without using the result from the pilot study of observed 50 observations, determine how big a sample of measurements should be if it is desirable to estimate the population proportion of satisfactory measurement within ±0.03

Answer 1

a. Here it is given that Of the 50 measurements, 37 were satisfactory.

So

b. For 95% CI, z value is 1.96 as P(-1.96<z<1.96)=0.95

So Margin of Error is

Hence CI is

c. Here for E=0.03, we get

d. Here we are given E=0.03 and we need to use p=0.5

So