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Identifying Parameters and Statistics

Parameters are numbers that summarize data for an entire population. Statistics are numbers that summarize data from a sample, i.e. some subset of the entire population.

 

Problems (1) through (6) below each present a statistical study*. For each study, identify both the parameter and the statistic in the study.

 

1) A researcher wants to estimate the average height of women aged 20 years or older. From a simple random sample of 45 women, the researcher obtains a sample mean height of 63.9 inches.

2) A nutritionist wants to estimate the mean amount of sodium consumed by children under the age of 10. From a random sample of 75 children under the age of 10, the nutritionist obtains a sample mean of 2993 milligrams of sodium consumed.

3) Nexium is a drug that can be used to reduce the acid produced by the body and heal damage to the esophagus. A researcher wants to estimate the proportion of patients taking Nexium that are healed within 8 weeks. A random sample of 224 patients suffering from acid reflux disease is obtained, and 213 of those patients were healed after 8 weeks.

4) A researcher wants to estimate the average farm size in Kansas. From a simple random sample of 40 farms, the researcher obtains a sample mean farm size of 731 acres.

5) An energy official wants to estimate the average oil output per well in the United States. From a random sample of 50 wells throughout the United States, the official obtains a sample mean of 10.7 barrels per day.

6) An education official wants to estimate the proportion of adults aged 18 or older who had read at least one book during the previous year. A random sample of 1006 adults aged 18 or older is obtained, and 835 of those adults had read at least one book during the previous year.

7) The International Dairy Foods Association (IDFA) wants to estimate the average amount of calcium male teenagers consume. From a random sample of 50 male teenagers, the IDFA obtained a sample mean of 1081 milligrams of calcium consumed.

8) A sociologist wants to the proportion of adults with children under the age of 18 that eat dinner together 7 nights a week. A simple random sample of 1122 adults with children under the age of 18 was obtained, and 337 of those adults reported eating dinner together with their families 7 nights a week.

9) A school administrator wants to estimate the mean score on the verbal portion of the SAT for students whose first language is not English. From a simple random sample of 20 students whose first language is not English, the administrator obtains a sample mean SAT verbal score of 458.

* These research objectives were adapted from problems in Michael Sullivan, Fundamentals of Statistics, 2nd edition, Pearson Education 2008.

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