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Difficulty: Very hardCalculating with Data

A microbiologist measured the bacterial growth rate (in cells/mL⋅hr\text{cells/mL}\cdot\text{hr}) of a newly isolated strain across three independent trials under four different incubator temperatures, as presented in the table below:

Temperature (∘C^\circ\text{C})Trial 1 (cells/mL⋅hr\text{cells/mL}\cdot\text{hr})Trial 2 (cells/mL⋅hr\text{cells/mL}\cdot\text{hr})Trial 3 (cells/mL⋅hr\text{cells/mL}\cdot\text{hr})
25140155125
30280310250
35420460380
40210240180

True or False: The mean growth rate at 35∘C35^\circ\text{C} exceeds the mean growth rate at 30∘C30^\circ\text{C} by more than 130 cells/mL⋅hr130\text{ cells/mL}\cdot\text{hr}.

Answer: Answer

Answer

The statement is True because the mean growth rate at 35∘C35^\circ\text{C} (420 cells/mL⋅hr420\text{ cells/mL}\cdot\text{hr}) exceeds the mean growth rate at 30∘C30^\circ\text{C} (280 cells/mL⋅hr280\text{ cells/mL}\cdot\text{hr}) by 140 cells/mL⋅hr140\text{ cells/mL}\cdot\text{hr}, which is greater than 130 cells/mL⋅hr130\text{ cells/mL}\cdot\text{hr}.
The mean growth rate at 35∘C35^\circ\text{C} is 420 cells/mL⋅hr420\text{ cells/mL}\cdot\text{hr} and at 30∘C30^\circ\text{C} is 280 cells/mL⋅hr280\text{ cells/mL}\cdot\text{hr}. The difference is 140 cells/mL⋅hr140\text{ cells/mL}\cdot\text{hr}, which is strictly greater than 130 cells/mL⋅hr130\text{ cells/mL}\cdot\text{hr}.

Step-by-Step Solution

1
Calculate the average growth rate for 35∘C35^\circ\text{C} across all three trials.
Mean35=420+460+3803=12603=420 cells/mL⋅hr\text{Mean}_{35} = \frac{420 + 460 + 380}{3} = \frac{1260}{3} = 420\text{ cells/mL}\cdot\text{hr}
Determining the representative data point for the 35∘C35^\circ\text{C} temperature condition requires finding the mean.
2
Calculate the average growth rate for 30∘C30^\circ\text{C} across all three trials.
Mean30=280+310+2503=8403=280 cells/mL⋅hr\text{Mean}_{30} = \frac{280 + 310 + 250}{3} = \frac{840}{3} = 280\text{ cells/mL}\cdot\text{hr}
Determining the representative data point for the 30∘C30^\circ\text{C} temperature condition requires finding the mean.
3
Subtract the mean rate at 30∘C30^\circ\text{C} from the mean rate at 35∘C35^\circ\text{C}.
420−280=140 cells/mL⋅hr420 - 280 = 140\text{ cells/mL}\cdot\text{hr}
Finding the increase in average growth rate between the two temperature conditions.
4
Compare the calculated difference (140 cells/mL⋅hr140\text{ cells/mL}\cdot\text{hr}) to the value given in the statement (130 cells/mL⋅hr130\text{ cells/mL}\cdot\text{hr}).
140>130140 > 130, so the statement is True.
Verifying whether the statement's inequality holds.

Key Concept

Calculating multi-trial averages and evaluating differences between data sets.
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Topics

Calculating with Data

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