A scientist experiments with mold colonies of equal area. She adds a treatment to half of the colonies. After a week, she measures the area of each colony. If the areas are significantly different, the scientist will repeat the experiment. The results are shown. Should the scientist repeat the experiment? Justify your answer.

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Solution

Step :Justification.
Order of Data of untreated Mold = $2 3 4 5 6 7$
Median of untreated Mold = = 4.5 $4 + 5 \div 2 = 9 \div 2 = 4.5$
IQR of untreated Mold = $4 - 2 = 2$
Order of Data of treated Mold = $0 1 2 3 6$
Median of treated Mold = $2$
IQR of treated Mold = $2 - 0 = 2$
Because the variables are same, you can describe the overlap in areas by expressing the difference in the medians as a multiple of the IQR.
Difference in Medians $\div$ IQR $4.5 - 2 \div 2$
$= 2.5 \div 2 = 1.25$
Because the quotient is less than $2$ , the differences in the medians is not significant.
The areas are not significantly greater than one and other colony.
Therefore, Yes the scientist should repeat the experiment because areas are significantly different from one to other.

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