Question

A researcher did a study looking at the effectiveness of different approaches to washing leafy green produce, with the goal of reducing risk for Escherichia coli (e coli) exposure in consumers. Farms were randomly assigned to either an enhanced washing regimen for three months, or to an industry-standard washing approach for the same amount of time. Periodically a member of a research team would visit each farm and obtain a sample of leafy greens for testing. The primary measure collected was the total number (count) of e-coli tainted samples collected from each farm over the three month period. There were 16 farms assigned randomly to each group. The distributions of e coli counts are below.

Typical washing: 6, 5, 9, 1, 0, 6, 2, 19, 3, 2, 1, 0, 1, 3, 6, 5

Enhanced washing: 2, 0, 3, 0, 0, 6, 3, 2, 0, 3, 0, 2, 2, 3, 1, 0

Go through the process of testing the hypothesis that the enhanced washing led to decreased levels of e coli being detected. Make sure you are explicit about the steps of hypothesis testing, including what statistical test you are using and the degrees of freedom. Use a 5% level of significance. Provide a brief narrative summary of the finding of your hypothesis test.

Answer 1

Let be the mean of  the total number (count) of e-coli tainted samples collected from each farm over the three month period from the typical washing and be the mean of  the total number (count) of e-coli tainted samples collected from each farm over the three month period from the typical washing.

vs

The calculations are done in R. On L.H.S. is R code and on R.H.S. R output

The p-value is 0.02469 < 0.05, therefore we reject the null hypothesis and conclude that the enhanced washing led to decreased levels of e coli being detected.