Researchers are looking to see if a new eco-friendly cleanser assists with killi
ID: 3219299 • Letter: R
Question
Researchers are looking to see if a new eco-friendly cleanser assists with killing bacteria efficiently. They have cultured 14 petri dish plates of agar with E. coli. A control solution was added to 10 plates and the eco-friendly cleanser to the remaining 10 plates. After 42 hours, they counted the number of bacteria colonies remaining each dish, listed below. Conduct a hypothesis test to determine if there is a difference in efficiency between the eco-friendly and control solutions. Use alpha = 0.05 and assume the data are not normal. (Make sure to complete all hypothesis testing steps and be specific.)Explanation / Answer
Solution
Let X = Number of bacteria in colonies in plates with eco-friendly cleanser.
Y = Number of bacteria in colonies in plates with control solution
We are given X and Y are Normal, say X ~ N(µ1, 12) and Y ~ N(µ2, 22) where 12 and 22 are unknown.
We have a sample of n (7) observations on each of X and Y
Null Hypothesis; H0: µ1 = µ2 Vs Alternative: HA: µ1 µ2 [Note: Question asks only if there is difference and not making a comparative claim.]
Test Statistic: t = (Xbar - Ybar)/s{(2/n)}
where n = common sample size for X and Y and Xbar and Ybar are sample means of X and Y respectively and s2 = (s12 + s22)/2; s12 and s22 being the respective sample variances.
Under H0, t ~ t2n-2.
Computations: [given = 0.05]
Using the given data, Xbar = 25.143; Ybar = 28.857;
s12 = 129.809; s22 = 101.809; s2 = 115.809; s = 10.761 and t = - 0.646
From Table of t-distribution, t12, 0.025 = 2.179
Inference: H0 is accepted at 5% level of significance since |t| < t12, 0.025
Conclusion: Evidence is not sufficient to suggest that there is difference in mean efficiency between eco-friendly cleanser and control solution.
DONE
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.