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F an alternative analysis involves recoded the

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(f) An alternative analysis involves recoded the observations as “compliant” and “not compliant.” If we say a measurement is non-compliant when the dissolved oxygen is below 5.0 mg/l, how many non- compliant measurements do we have in this data set? What proportion of the sample is below 5.0 mg/l? [ Hint : What do you want to do with the observation that is equal to 5.0?] (g) Carry out a test for deciding whether the proportion of measurements that fall below 5.0 mg/l is statistically significantly larger than 0.50. (h) If you decide that more than half of the time the river is non-compliant (that is, more than 50% of measurements are below 5.0 mg/l), what does that imply about the long-run median dissolved oxygen level? Explain. (i) Identify one advantage to this analysis over the one-sample t -test. Identify one disadvantage of this analysis over the one-sample t -test.

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Chance/Rossman, 2015 ISCAM III Investigation 2.7 171 (j) The researchers actually wanted to decide whether the river was non-compliant more than 10% of the time. How would that change your analysis in (g) and would the p-value be larger or smaller? Study Conclusions Both the mean (not shown) and of the median indicate that dissolved oxygen in this river tended to below the 5.0 mg/l that was cited as t he “action level.” Although we don’t have statistically significant evidence that the long-run median DO level is below 5.0 (binomial p-value | 0.30), the researchers actually wanted to engage in remedial action if the river is found to be in non-compliance significantly more than 10% of the time. The exact binomial probability of observing 19 or more non-compliant values from a process with a 0.10 chance of non-compliance is 4.16 × 10 -11 , leaving “little doubt that the10% non-compliant criterion was exceeded at the monitoring site during 2000. Discussion : When we use 0.50 as the hypothesized probability of success and we count how many of our quantitative observations exceed some pre-specified level, this is called the sign test and corresponds to a test of whether the population median equals that pre-specified level. The sign test can be advantageous over the t -test if the validity conditions for the t -test are not met (e.g., skewness in sample, not a large sample size). However, although this procedure focuses on how often you are above or below that level, it does not provide information about how far above or below as a confidence interval for the mean could. Practice Problem 2.7 Return to Practice Problem 2.2A. Carry out a test to determine whether there is convincing evidence that the median student estimate of 30 seconds differs from 30. (State your hypothesis, statistic and/or test statistic, and p-value.)
Chance/Rossman, 2015 ISCAM III Investigation 2.8 172 Investigation 2.8: Turbidity Another measure of water quality is turbidity, the degree of opaqueness produced in water by suspended particulate matter. Turbidity can be measured by seeing how light is scattered and/or absorbed by organic and inorganic material.

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