Q1.
A researcher wishing to estimate the proportion of X-ray machines that malfunction and produce excess radiation. A random sample of 40 machines is taken and 12 of the machines malfunction. The problem is to compute the 95% confidence interval on π, the proportion that malfunction in the population.
Q2.
A manager at a power company monitored the employee time required to process high-efficiency lamp bulb rebates. A random sample of 40 applications gave a sample mean time of 3.8 minutes and a standard deviation of 1.2 minutes. Construct a 90% confidence interval for the mean time to process μ.
Q.3
The amount of PCBs (polychlorinated biphenyls) was measured in 40 samples of soil that were treated with contaminated sludge. The following summary statistics were obtained. x = 3.56, s = .5ppm Obtain a 95% confidence interval for the population mean μ, amount of PCBs in the soil.
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Radiation of microwave ovens has normal distribution with standard deviation σ=0.6. A sample of 25 microwave ovens produced X = 0.11. Determine a 95% confidence interval for the mean radiation.
Q5.
A manufacturer of pharmaceutical products analyzes a specimen from each batch of a product to verify the concentration of the active ingredient. The chemical analysis is not perfectly precise. Repeated measurements on the same specimen give slightly different results. The results of repeated measurements follow a normal distribution quite closely. The analysis procedure has no bias, so the mean μ of the population of all measurements is the true concentration in the specimen. The standard deviation of this distribution is known to be σ = .0068 grams per liter. The laboratory analyzes each specimen three times and reports the mean result. Three analyses of one specimen give concentrations
0.84030.83630.8447.
We want a 99% confidence interval for the true concentration μ. The sample mean of the three readings is
.8403 + .8363 + .8447
x = —————————– = .8404.
3
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