Solve for x: (5 points)
1 answer:
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Answer: -8.16 to 15.84
Step-by-step explanation: <u>Confidence</u> <u>Interval</u> is an interval in which we are a percentage sure the true mean is in the interval.
A confidence interval for a difference between two means and since sample 1 and sample 2 are under 30, will be
±
where
x₁ and x₂ are sample means
t is t-score
is estimate of standard deviation
n₁ and n₂ are the sample numbers
The estimate of standard deviation is calculated as
where
s₁ and s₂ are sample standard deviation of each sample
Degrees of freedom is:
df = 12 + 9 - 2
df = 19
Checking t-table, with 90% Confidence Interval and df = 19, t = 1.729.
The mean and standard deviation for 12 unlogged forest plots are 17.5 and 3.53, respectively.
The mean and standard deviation for 9 logged plots are 13.66 and 4.5, respectively.
Calculating estimate of standard deviaton:
15.74
The difference between means is
= 17.5 - 13.66 = 3.84
Calculating the interval:
=
=
=
= 12
Then, interval for the difference in mean is 3.84 ± 12, which means the interval is between:
lower limit: 3.84 - 12 = -8.16
upper limit: 3.84 + 12 = 15.84
The interval is from -8.16 to 15.84.