Question

To investigate water quality, in early September 2016, the Ohio Department of Health took water samples at 2424 beaches on Lake Erie in Erie County. Those samples were tested for fecal coliform, which is the E.coli bacteria found in human and animal feces. An unsafe level of fecal coliform means there is a higher chance that disease‑causing bacteria are present and more risk that a swimmer will become ill if she or he should accidentally ingest some of the water. Ohio considers it unsafe for swimming if a 100100‑milliliter sample (about 3.43.4 ounces) of water contains more than 400400 coliform bacteria. The E. colilevels found 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

To access the complete data set, click the link for your preferred software format:

Excel  Minitab  JMP  SPSS TI  R  Mac-TXT   PC-TXT  CSV  CrunchIt!

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

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

?⎯⎯⎯=x¯=

?=s=

?=t=

Find the ?-valueP-value . (Enter your answer rounded to four decimal 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 in Erie County have mean E. coli counts less than 400400 bacteria per 100100 mL.

The data gives us no conclusive evidence one way or the other.

There is good evidence to conclude that swimming areas in Erie County have mean E. coli counts less than 400400 bacteria per 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‑values without assuming any specific shape for the distribution gives a ?P‑value of 0.00430.0043 to answer if the given data shows average E.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 procedures should not be used here.

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

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

What does the ?P‑value from the method that does not assume any specific shape for the distribution indicate?

The method that does not assume a specific shape for the distribution provides very little evidence that these swimming areas are safe on average.

The method that does not assume a specific shape for the distribution provides very strong evidence that these swimming areas are safe on average.

The method that does not assume a specific shape for the distribution provides very strong evidence that these swimming areas are not safe on average.

Answer 1

18.7
19.9
365.4
579.4
83.6
238.2
1986.3
365.4
209.8
517.2
307.6
290.9
98.7
285.1
137.6
45.7
152.9
1046.2
124.6
18.7
127.4
201.4
151.5
224.7
mean	316.5375
SD	420.9057

There is not good evidence to conclude that swimming areas in Erie County have mean E. coil counts less than 400 bacteria per 100 mL

b)

P‑value of 0.0043

From above test P-value = 0.1707

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

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

The method that does not assume a specific shape for the distribution provides very strong evidence that these swimming areas are safe on average.