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Staph Infections. In the article "Using EDE, ANOVA and Regression to Optimize Some Microbiology Data" (Journal of Statistics Education, Vol. $12$, No. 2, online), N. Binnie analyzed bacteria culture data collected by G. Cooper at the Auckland University of Technology. Five strains of cultured Staphylococcus aureus bacteria that cause staph infections were observed for $24$hours at ${27}^{o}C$. The following table reports bacteria counts, in millions, for different cases from each of the five strains.

At the $5\%$significance level, do the data provide sufficient evidence to conclude that a difference exists in mean bacteria counts among the five strains of Staphylococcus aureus? (Note: $T_1=104,T_2=129$, $T_3=185,T_4=98,T_5=194$,$\mathrm{Î\pounds }{x^2}_i=25,424$.)

Step by step solution

01

Given information

The given table is

$T_1=104$

$T_2=129$

$T_3=185$

$T_4=98$

role="math" localid="1652185103283" $T_5=194$

$\mathrm{Î\pounds }{x_i}^2=25,424$.

02

Explanation

The hypothesis is

$H_0:{\mathrm{μ}}_1={\mathrm{μ}}_2={\mathrm{μ}}_3={\mathrm{μ}}_4={\mathrm{μ}}_5$

$H_a:$Not all the mean are equal

The value of $\mathrm{Î\pm }=0.05$

Using the given values find the value of the test statistic

$\mathrm{F}=\mathrm{MSTR}/\mathrm{MSE}$

$F=2.23$

The value of critical value is $2.87$

Here the test statistic $<$critical value

$P(P=0.103)>0.10$

It usually does not reject $H_0$.

At the $5\%$level, the data on bacteria number among the $5$ distinct staphylococcus aureus strains does not provide enough information to draw the conclusion that there is a difference in mean bacteria number among the $5$ different staphylococcus aureus strains.

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