Group Problems - Confidence IntervalsCIVL 3103

1 1. The average zinc concentration recovered from a sample of zinc measurements in 36different locations is found to be 2.6 grams per milliliter. Assume that the populationstandard deviation is OJ.

a. Find a 95% confidence interval for the mean zinc concentration in the river.b. Find a 99% confidence interval for the mean zinc concentration in the river.c. How large a sample is required if we want to be 95% confident that our estimate of

Il is offby less than 0.05?

., 2. A study published in Chemosphere reported levels of the dioxin TCDD of20 MassachusettsVietnam veterans who were possibly exposed to Agent Orange. The amount of TCDDlevels in plasma and fat tissue are listed in the table below. Find a 95% confidence intervalfor III - 1l2, where III and 112represent the true mean TCDD in plasma and in fa! tissue,respectively. Assume the distribution of the differences to be approximately normal,

TCDD levels in plasma TCDD levels in fat tissueVeteran1234567891011121314151617181920

2.53.12.13.53.11.86.03.036.04.76.93J4.61.67.21.8

20.02.02.54.1

4.95.94.46.97.04.210.05.5

41.04.47.02.94.61.47.71.111.02.52.32.5

, .

Two chemical companies can supply a raw material. The concentration of a particularelement in this material is important. The mean concentration for both suppliers is the same,but we suspect that the variability in concentration may differ between the two companies.The standard deviation of concentration in a random sample n, = 10 batches produced bycompany 1 is s, = 4.7 grams per liter, while for company 2, a random sample of n2 = 16batches yields S2= 5.8 grams per liter. Find a 95 % confidence on the ratio of the variances.

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