Question

One website considers it unsafe if a 100-milliliter sample (about 3.3 ounces) of water contains more than 400 coliform bacteria. Here are part of the data for the fecal coliform levels found by laboratories at 20 Ohio State Park swimming areas: (Source: Moore/Notz/Eligner, The Basic Practice of Statistics, 8e, 2018) 248 164 37 30 146 13 19 144 66 242 236 ... 20... (x = 113.75 and s = 93.9) Are these data good evidence that, on average, the fecal coliform levels in these swimming areas were unsafe? a. Specify the following: i. random variable of interest: ii. parameter of interest (Symbol for the parameter) iii. statistic used to estimate parameter o S p P other: other: Ī b. Identify the hypotheses of interest investigated by the researchers of the study, according to the information given above. A. Ho: parameter = constant vs Ha: parameter constant B. Ho: parameter = constant vs Ha: parameter < constant C. Ho: parameter = constant vs Ha: parameter > constant C. Select the sketch you would use to find the P-value, and indicate important points if the value of the test statistic is 0.95.

Answer 1

a) We want to test if on average the fecal coliform levels were unsafe.

i) Random variable here will me the sample average

Note that population average is a constant and not a random variable.

Therefore, random variable of interest is  $\overline{x}$.

ii) The parameter of interest is the population mean because we are trying to estimate the population mean based on the samples.

Therefore, parameter of interest is  $\mu$

iii) Population mean will be estimated using sample mean.

Therefore, statistic used is $\overline{x}$

b) We can conclude that the fecal coliform levels in water is unsafe if, on average, it contains more than 400 bacteria.

Therefore, the hypothesis of interest is.

$H_0:\mu=400$

H, :μ> 400

Option C.

c) We will reject Ho for high values of sample mean i.e high mean coliform levels. Therefore, the rejection region will be to the right(high values)

Option iii