2x + 4y = 2 3x + 2y = 11
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Answer:
The 95% confidence interval for the mean breaking weight for this type cable is (767.47 lb, 777.13 lb).
Step-by-step explanation:
Our sample size is 41
The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So
Then, we need to subtract one by the confidence level and divide by 2. So:
Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 40 and 0.025 in the two-sided t-distribution table, we have
Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So
Now, we multiply T and s
Then
The lower end of the confidence interval is the mean subtracted by M. So:
The upper end of the confidence interval is the mean added to M. So:
The 95% confidence interval for the mean breaking weight for this type cable is (767.47 lb, 777.13 lb).