That the mean may not be the parameter we are most

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that the mean may not be the parameter we are most interested in and/or may not even be possible to calculate depending on the form of the data. In this section, you will look at a possible inference procedure when the median is of interest, as well as a newer methodology that works for any statistic of your choosing. Investigation 2.7: Water Oxygen Levels Scientists often monitor the “health” of water system s to determine the impact of different changes in the environment. For example, Riggs (2002) reports on a case study that monitored the dissolved oxygen downstream from a commercial hog operation. There had been problems at this site for several years (e.g., manure lagoon overflow), including several fish deaths in the previous three years just downstream of a large swale through which runoff from the hog facility had escaped. The state pollution control agency decided to closely monitor dissolved oxygen downstream of the swale for the next three years to determine whether the problem had been resolved. In particular, they wanted to see whether there was a tendency for the dissolved oxygen level in the river to be less than the 5.0 mg/l standard. Sampling was scheduled to commence in January of 2000 and run through December of 2002. The monitors took measurements at a single point in the river, approximately six tenths of a mile from the swale, once every 11 days. (a) Identify the observational units in this study. Would you consider this sampling from a population or from a process? (b) Because the dissolved oxygen measurements were taken in the same location at fixed time intervals, would you consider this a simple random sample? Do you think the sample is likely to be representative of the river conditions? Explain. Definition: A systematic sample takes selects observations at fixed intervals (e.g., every 10 th person in line). If the initial observation is chosen at random and there is no structure in the data matching up to the interval size (e.g., every 7 th day), then such samples are generally assumed to be representative of the population. In fact, we will often simplify the analysis by assuming they behave like simple random samples. (c) Examine the data from the first year in WaterQuality.txt . Describe the shape, center, and variability of the distribution. In particular, how do the mean and median compare? Do these data appear to be well-modelled by a normal distribution?
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Chance/Rossman, 2015 ISCAM III Investigation 2.7 170 (d) State the null and alternative hypotheses for testing whether the long-run mean dissolved oxygen in this river is less than 5.0 mg/l (indicating too little oxygen in the water, causing problems in the aquatic community structure). (e) Is the one-sample t -test likely to be valid for these data? Explain why or why not.
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