A 180 ft long board is cut into 3 pieces. The second piece of board is twice as long as the first. The third piece of board is s
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Answer: The confidence interval will be -91.87 < μ₁-μ₂ <751.87
Step-by-step explanation: <u>Confidence</u> <u>Interval</u> is the interval of certainty in which the true population mean is in.
In a confidence interval for the difference between two averages with a sample size less than 30, the calculations are:
±
in which
x₁ and x₂ are the sample mean of each data set
t is the probability found in the t-table whose df = n₁ + n₂ - 2
is the pooled estimate of the common standard deviation, assuming variances are similar, and can be calculated as:
n₁ and n₂ are sample sizes
The data to construct the interval are:
Mine A:
x₁ = 8260
s₁ = 251.9
n₁ = 5
Mine B:
x₂ = 7930
s₂ = 206.52
n₂ = 5
Then:
230.33
Using a table, for a 99% confidence and df = 8, t-score = 2.896.
Doing calculations:
(8260-7930) ± (2.896)(230.33)()
330 ± (2.896)(230.33)()
330 ± 421.87
Interval will be
A 99% confidence interval for the difference between the true average heat-producing capacities of coal from the mines is between -91.87 and 751.87