To investigate water quality, in early September 2016, the OhioDepartment of Health took water samples at 2424 beaches on LakeErie in Erie County. Those samples were tested for fecal coliform,which is the E.coli bacteria found in human and animalfeces. An unsafe level of fecal coliform means there is a higherchance that disease?causing bacteria are present and more risk thata swimmer will become ill if she or he should accidentally ingestsome of the water. Ohio considers it unsafe for swimming if a100100?milliliter sample (about 3.43.4 ounces) of water containsmore than 400400 coliform bacteria. The E. colilevelsfound by the laboratories are shown in the table.

18.718.7	579.4579.4	1986.31986.3	517.2517.2	98.798.7	45.745.7	124.6124.6	201.4201.4
19.919.9	83.683.6	365.4365.4	307.6307.6	285.1285.1	152.9152.9	18.718.7	151.5151.5
365.4365.4	238.2238.2	209.8209.8	290.9290.9	137.6137.6	1046.21046.2	127.4127.4	224.7224.7

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Take these water samples to be an SRS of the water in allswimming areas in Erie County. Let ?? represent the mean E.colicounts for all possible 100100?mL samples taken from allswimming areas in Erie County. We test ?0:?=400 versus??:?<400H0:?=400 versus Ha:?<400 because the researchers areinterested in whether the average E. coli levels in theseareas are safe.

(a) Find ????x¯ , ?s , and the ?t statistic. (Enter your answersrounded to three decimal places)

????=x¯=

?=s=

?=t=

Find the ?-valueP-value . (Enter your answer rounded to fourdecimal places.)

??value=P?value=

Are these data good evidence that on average the E.coli levels in these swimming areas were safe?

There is not good evidence to conclude that swimming areas inErie County have mean E. coli counts less than 400400bacteria per 100100 mL.

The data gives us no conclusive evidence one way or theother.

There is good evidence to conclude that swimming areas in ErieCounty have mean E. coli counts less than 400400 bacteriaper 100100mL.

(b) Use the software of your choice to make a graph of the data.The distribution is very skewed. Another method that gives?P?valueswithout assuming any specific shape for the distribution gives a?P?value of 0.00430.0043 to answer if the given data shows averageE.coli levels were safe in the swimming areas.

How does the one?sample ?t test compare with this?

The one?sample ?t test gives a significantly higher?P?value.

Both methods give similar ?P?values.

The one?sample ?t test gives a significantly lower ?P?value.

Should the ?t procedures be used with these data?

Due to extreme skew and the presence of outliers, ?t proceduresshould not be used here.

Due to symmetry and the absence of outliers, ?t proceduresshould be used here.

Due to symmetry and the absence of outliers, ?t proceduresshould not be used here.

What does the ?P?value from the method that does not assume anyspecific shape for the distribution indicate?

The method that does not assume a specific shape for thedistribution provides very little evidence that these swimmingareas are safe on average.

The method that does not assume a specific shape for thedistribution provides very strong evidence that these swimmingareas are safe on average.

The method that does not assume a specific shape for thedistribution provides very strong evidence that these swimmingareas are not safe on average.