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Chapter 6: Q85E (page 367)
Suppose you want to estimate a population proportion,,and,,and.Find an approximate 95% confidence interval for.
The approximate confidence interval for is
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Crude oil biodegradation. Refer to the Journal of Petroleum Geology (April 2010) study of the environmental factors associated with biodegradation in crude oil reservoirs, Exercise 2.29 (p. 85). One indicator of biodegradation is the level of dioxide in the water. Recall that 16 water specimens were randomly selected from various locations in a reservoir on the floor of a mine and the amount of dioxide (milligrams/liter) as well as presence of oil was determined for each specimen. These data are reproduced in the next table.
a. Estimate the true mean amount of dioxide present in water specimens that contain oil using a 95% confidence interval. Give a practical interpretation of the interval.
b. Repeat part a for water specimens that do not contain oil.
c. Based on the results, parts a and b, make an inference about biodegradation at the mine reservoir.
A random sample of 50 consumers taste-tested a new snack food. Their responses were coded (0: do not like; 1: like; 2: indifferent) and recorded as follows:
a. Use an 80% confidence interval to estimate the proportion of consumers who like the snack food.
b. Provide a statistical interpretation for the confidence interval you constructed in part a.
The following random sample was selected from a normal distribution: 4, 6, 3, 5, 9, and 3.
Suppose you wish to estimate a population mean correct to within .20 with probability equal to .90. You do not know , but you know that the observations will range in value between 30 and 34.
a. Find the approximate sample size that will produce the desired accuracy of the estimate. You wish to be conservative to ensure that the sample size will be ample to achieve the desired accuracy of the estimate. [Hint: Using your knowledge of data variation from Section 2.6, assume that the range of the observations will equal 4.]
b. Calculate the approximate sample size, making the less conservative assumption that the range of the observations is equal to .
In each case, find the approximate sample size required to construct a 95% confidence interval for p that has sampling error of SE = .08.
a. Assume p is near .2.
b. Assume you have no prior knowledge about p, but you wish to be certain that your sample is large enough to achieve the specified accuracy for the estimate.
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