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Answer:
The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).
Step-by-step explanation:
We have to calculate a 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams.
The sample 1 (Fiberglass), of size n1=26 has a mean of 33.4 and a standard deviation of 2.2.
The sample 2 (Carbon), of size n2=26 has a mean of 42.8 and a standard deviation of 4.3.
The difference between sample means is Md=-9.4.
The estimated standard error of the difference between means is computed using the formula:
The critical t-value for a 99% confidence interval is t=2.678.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).