Population of water resources is a serious problem that can require substantial
ID: 3253466 • Letter: P
Question
Population of water resources is a serious problem that can require substantial efforts to improve. To determine the financial resources required, an accurate assessment of the extent of the problem is needed. The index of biotic integrity (IBI) is a measure of the water quality in streams. Here are IBI measurements for a sample of streams in the Ozark Highland ecoregion of Arkansas that were collected as part of a study:
47 61 39 59 72 76 85 89 74 89 33 46 32 80 80 78 53 43 88 84 62 55 29 29 54 78 71 55 58 71 33 59 81 71 75 64 41 82 60 84 83 82 82 86 79 67 56 85 91
Give a 95% confidence interval for the mean IBI for streams in the Ozark Highland ecoregion of Arkansas that were sampled in this study.
Interpret the 95% CI in the context of the problem.
Do we need to assume normality for this problem? Why or why not?
Explanation / Answer
The statistical software output for 95% confidence interval is:
One sample T confidence interval:
: Mean of variable
95% confidence interval results:
Hence,
95% confidence interval will be:
(60.688, 71.189)
Interpretation:
We are 95% confident that the true mean for streams in the Ozark Highland ecoregion of Arkansas lie between 61 and 71.
No, we do not need to assume normality because the sample size is greater than 30 and hence, the distribution of the mean will be normal according to the central limit theorem, regardless of the distribution of original population.
Variable Sample Mean Std. Err. DF L. Limit U. Limit var1 65.938776 2.6113645 48 60.688275 71.189276