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(12 −− 9.6 mm) 2 ++ (8 −− 9.6 mm) 2 ++ (15 −− 9.6mm) 2 ++ (13 −− 9.6 mm) 2 ++ (6 −− 9.6 mm) 2
++ (4 −− 9.6mm) 2 ++ (13 −− 9.6 mm) 2 ++ (14 −− 9.6mm) 2 ++ (5 −− 9.6mm) 2 ++ (6 −− 9.6mm) 2
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s ==
10 −− 1
158.4mm
s == == 4.20 mm
9
Light:

∑∑ ( x i −− ) 2
x
s ==
n −− 1
(18 −− 18.4mm) 2 ++ (22 −− 18.4mm) 2 ++ (17 −− 18.4mm) 2 ++ (23 −− 18.4mm) 2 ++ (16 −− 18.4mm) 2
−−
−−
−−
++ (18 −− 18.4mm) 2 ++ (22 −− 18.4mm) 2 ++ (12 18.4mm) 2 ++ (19 18.4mm) 2 ++ (17 18.4mm) 2
s ==
10 −− 1
98.4mm
s == == 3.31mm
9
The standard deviation of the heights for seedlings grown in the dark is 4.20 mm, and the standard
deviation of the heights for seedlings grown in the light is 3.31 mm.

3. Calculate the standard error of the mean of the heights of the seedlings grown in the dark and the
light.

Because we have just found the standard deviation for each treatment (s) and we know the sample
size (n) for each treatment as well, we can plug these into the formula for the standard error of the
mean:

s 4.20 mm
Dark: SE x == SE x == SE x == 1.33 mm
n 10
s 3.31mm
Light: SE x == SE x == SE x == 1.05 mm
n 10

The standard error of the mean of the heights for seedlings in the dark is 1.33 mm. The standard
error of the mean of the heights for seedlings in the light is 1.05 mm.

4. Calculate the 95% confidence interval of the mean of the heights of the seedlings grown in the dark
and the light.

The 95% confidence interval represents a range of values where the true mean is likely to be found.
On a graph, this range is often portrayed with error bars. To calculate the 95% confidence interval,
we will use the mean and standard error of the mean.

95% confidenceinterval == x ±± 2 SE x
Dark: 9.6mm ±± (2 ×× 1.33mm) →→ 9.6mm ±± 2.66mm
The 95% confidence interval of the mean for seedlings grown in the dark is 9.6 ± 2.66mm. This can
also be written as the range of values itself: 7.0–12.2 mm. On a graph, an error bar is drawn from
6.94 mm to 12.26 mm to represent the 95% confidence interval. We can be 95% sure that the confi-
dence interval includes the true mean length of growth for seedlings grown in the dark.
Light: 18.4mm ±± (2 ×× 1.05mm) →→ 18.4mm ±± 2.10mm

The 95% confidence interval of the mean for seedlings grown in the light is 18.4 ± 2.10mm. This can
also be written as the range of values itself: 16.3–20.5 mm. On a graph, an error bar is drawn from
16.3 mm to 20.5 mm to represent the 95% confidence interval. We can be 95% sure that the confi-
dence interval includes the true mean length of growth for seedlings grown in the light.
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MODULE 1 ELEMENTS OF LIFE 29

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