2-Sample t-Test (normal populations and equal variances) Consider an experiment

Question

2-Sample t-Test (normal populations and equal variances) Consider an experiment where medical researchers wish to test the efficacy of a new antibiotic, labeled A. They will compare it to the old gold-standard antibiotic labeled B for which there is not yet any known resistance. To conduct the test, the researchers will prepare several agar plates. As the antibiotics themselves are produced by modified bacteria, the plates will be steralized and seeded with both e-Coli and either the bacteria producing antibiotic A and antibiotic B. After 5 days, the percentage of e-Coli (out of total bacteria on the plate) is measured: A: 0.13, 0.12, 0.14, 0.07, 0.21, 0.13, 0.08, 0.25, 0.14, 0.12 B: 0.24, 0.24, 0.13, 0.15, 0.20, 0.26, 0.19, 0.12, 0.13, 0.17 1. What problems might exist in analyzing this particular experiment? 2. If we ignore these problems, what is the appropriate set of hypotheses? est should we pertorm and why 4. Conduct the test. What is the rejection region and/or p-value? Do we reject?

Explanation / Answer

we can perform a 2 independent samples t test as both the sets of observations are for 2 different drugs which are independent of one another

we can analyse this in the open source statistical package to see if the ecoli is less in A

A <- c(0.13,0.12,0.14,0.07,0.21,0.13,0.08,0.25,0.14,0.12)
B <- c(0.24,0.24,0.13,0.15,0.20,0.26,0.19,0.12,0.13,0.17)

# t test
t.test(A,B,alternative = "less",conf.level=0.95)

The results are

> t.test(A,B,alternative = "less",conf.level=0.95)

   Welch Two Sample t-test

data: A and B
t = -1.8649, df = 17.941, p-value = 0.03932 ## as the p value is less than 0.05 , hence we reject the null hypothesis
alternative hypothesis: true difference in means is less than 0
95 percent confidence interval:
-Inf -0.003079551
sample estimates:
mean of x mean of y
0.139 0.183

H0 : The mean value of ecoli in A is not less than mean ecoli of B

H1 : The mean value of ecoli in A is signficantly less than mean ecoli of B

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