Chapter 6: Q7E (page 339)
Explain the difference between an interval estimator and a point estimator for
A random variable is an estimator, as well as a value, is an estimation that represents the estimator's calculated number.
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General health survey. The Centres for Disease Control and Prevention (CDCP) in Atlanta, Georgia, conducts an annual survey of the general health of the U.S. population as part of its Behavioural Risk Factor Surveillance System. Using random-digit-dialing, the CDCP telephones U.S. citizens over 18 years of age and asks them the following four questions:
1. Is your health generally excellent, very good, good, fair, or poor?
2. How many days during the previous 30 days was your physical health not good because of injury or illness?
3. How many days during the previous 30 days was your mental health not good because of stress, depression, or emotional problems?
4. How many days during the previous 30 days did your physical or mental health prevent you from performing your usual activities?
Identify the parameter of interest for each question
In each of the following instances, determine whether you would use a z- or t-statistic (or neither) to form a 90%confidence interval and then state the appropriate z- ort-statistic value for the confidence interval.
a. Random sample of size n = 32 from a normal distribution with a population mean of 60 and population standard deviation of 4.
b. Random sample of size n = 108 from an unknown population.
c. Random sample of size n = 12 from a normal distribution witha sample mean of 83 and sample standard deviation of 2.
d. Random sample of size n = 24 from a normal distribution withan unknown mean and sample standard deviation of 3.
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° using a vacuum fryer. One characteristic of interest to the researchers was internal oil content (measured in millions of grams). The results were: and . 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 .
c. What does it mean to say that the target parameter lies within the interval with “95% confidence”?
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, , is desired.
f. Use the results, part b, to compute a 95% confidence interval for . Give a practical interpretation of the interval.
Methyl t-butyl ether (MTBE) is an organic water contaminant that often results from gasoline spills. The level of MTBE (in parts per billion) was measured for a sample of 12 well sites located near a gasoline service station in New Jersey (Environmental Science & Technology,January 2005). The data are listed in the accompanying table.
a. Give a point estimate for m, the true mean MTBE level for all well sites located near the New Jersey gasoline service station.
b. Calculate and interpret a 99% confidence interval for m.
c. What assumptions are required for the interval, part b, to be valid? Are these assumptions reasonably satisfied?
If nothing is known about p, .5 can be substituted for p in the sample size formula for a population proportion. But when this is done, the resulting sample size may be larger than needed. Under what circumstances will be using p = .5 in the sample size formula yield a sample size larger than needed to construct a confidence interval for p with a specified bound and a specified confidence level?
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