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Answer:
The 90% confidence interval is (64.0101, 68.9899).
Step-by-step explanation:
Our sample size is 310.
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 309 and 0.05 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
LCL is the mean subtracted by M. So:
UCL is the mean added to M. So:
The 90% confidence interval is (64.0101, 68.9899).