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Chapter 6: Q117SE (page 376)

Water pollution testing. The EPA wants to test a randomlyselected sample of n water specimens and estimate themean daily rate of pollution produced by a mining operation.If the EPA wants a 95% confidence interval estimatewith a sampling error of 1 milligram per liter (mg/L),how many water specimens are required in the sample?Assume prior knowledge indicates that pollution readingsin water samples taken during a day are approximately

normally distributed with a standard deviation equal to5 mg/L.

Short Answer

Expert verified

The number of water specimens required in the sample are n=97.

Step by step solution

01

Given Information

In water pollution testing the EPA is randomly selecting a sample with n water specimens to estimate the mean daily rate of pollution. The EPA wants a confidence interval of 95% level of significance with a sampling error of 1 mg/L.

The prior knowledge tells that the sample standard deviation is 5mg/L.

02

Step 2:Defining the parameters

Therefore, the parameters here are:

蟽=5mg/LS.E.=1mg/LCI=0.95

Now, the formula for sampling error is:

S.E.=z脳蟽n

Also, the z value for 0.95 confidence interval is 1.96

Step 2:Substituting the values

S.E.=z脳蟽n1=1.96脳5nn=9.8n=96.04n鈮�97

Therefore, n=97 water specimens are required

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Most popular questions from this chapter

The following sample of 16 measurements was selected from a population that is approximately normally distributed:

  1. Construct an 80% confidence interval for the population mean.
  2. Construct a 95% confidence interval for the population mean and compare the width of this interval with that of part a.
  3. Carefully interpret each of the confidence intervals and explain why the 80% confidence interval is narrower.

Radon exposure in Egyptian tombs. Refer to the Radiation Protection Dosimetry (December 2010) study of radon exposure in tombs carved from limestone in the Egyptian Valley of Kings, Exercise 6.30 (p. 349). The radon levels in the inner chambers of a sample of 12 tombs were determined, yielding the following summary statistics: x炉=3643Bq/m3and s=4487Bq/m3. Use this information to estimate, with 95% confidence, the true standard deviation of radon levels in tombs in the Valley of Kings. Interpret the resulting interval.

Oil content of fried sweet potato chips. The characteristics of sweet potato chips fried at different temperatures were investigated in the Journal of Food Engineering (September 2013). A sample of 6 sweet potato slices was fried at 130掳 using a vacuum fryer. One characteristic of interest to the researchers was internal oil content (measured in millions of grams). The results were: x炉=178and s=11. The researchers are interested in estimating the variance of the interval oil content measurements for sweet potato chips.

a. Identify the target parameter, in symbols and words.

b. Compute a 95% confidence interval for 蟽2.

c. What does it mean to say that the target parameter lies within the interval with 鈥�95% confidence鈥�?

d. What assumption about the data must be satisfied in order for the confidence interval to be valid?

e. To obtain a practical interpretation of the interval, part b, explain why a confidence interval for the standard deviation, 蟽, is desired.

f. Use the results, part b, to compute a 95% confidence interval for蟽 . Give a practical interpretation of the interval.

Study of aircraft bird-strikes. As worldwide air traffic volume has grown over the years, the problem of airplanes striking birds and other flying wildlife has increased dramatically. The International Journal for Traffic and Transport Engineering (Vol. 3, 2013) reported on a study of aircraft bird strikes at Aminu Kano International Airport in Nigeria. During the survey period, a sample of 44 aircraft bird strikes were analyzed. The researchers found that 36 of the 44 bird strikes at the airport occurred above 100 feet. Suppose an airport air traffic controller estimates that less than 70% of aircraft bird strikes occur above 100 feet. Comment on the accuracy of this estimate. Use a 95% confidence interval to support your inference.

Lett0 be a specific value of t. Use Table III in Appendix D to findt0 values such that the following statements are true.

a. 巍(t鈮�t0)=0.025where df=11

b.巍(t鈮�t0)=0.01 wheredf=9

c.巍(t鈮�t0)=0.005 wheredf=6

d.巍(t鈮�t0)=0.05 wheredf=18
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