Intravenous (IV) infusion fluids produced by three different pharmaceutical comp

Question

Intravenous (IV) infusion fluids produced by three different pharmaceutical companies (Abbott, Turnbull, and Hanson) were tested for their concentration of particulate contaminants measured as the number of particles larger than five microns in diameter per litre of IV fluid. Six samples were collected from each company, however one sample from Hanson was lost in transit. The concentrations of particulate contaminants for the 17 samples are given in the following table: (f) Test if there is any significant difference in the mean concentration of particulate contaminants for IV fluids produced by Abbott compared with Turnbull (show all working and include appropriate hypothesis statements).

Explanation / Answer

here we use t-test for testing of difference of two sample means(Abbott and Turnbull)

with null hypothesis H0:Abbott mean=Turnbull and

alternate hypothesis H1:Abbott mean is not =Turnbull

the statistic t=(mean1-mean2)/((sp*(1/n1 +1/n2)1/2) and sp2=((n1-1)s12+(n2-1)s22)/n and with df is n=n1+n2-2

since level of significance is not given let it is 0.05 ( generally alpha=0.05 is taken)

since two-tailed p-value=0.11 is more than alpha=0.05, we fail to reject H0 and conclude that there is not significant difference in the mean concentration produced by Abbott and Turnbull.

sample mean s s2 n (n-1)s2 Abbott 273.83 51.35 2636.8225 6 13184.1125 Turnbull 204.5 83.33 6943.8889 6 34719.4445 total= 478.33 9580.7114 12 47903.557 sp2= 4790.3557 sp= 69.21239557 t= 1.734993877 one tailed p-value= 0.056698779 two tailed p-value= 0.113397558 Abbott Turnbull 255 105 264 288 342 98 331 275 234 221 217 240 mean= 273.83 204.50 sample sd=s= 51.35 83.33

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