Answer :
Final answer:
To estimate the 99% confidence interval for the given data, first calculate the sample mean and standard deviation, then find the critical value from a Z table (for a 99% confidence interval, it's about 2.57), and lastly substitute these data into the formula for the confidence interval. Do not round-off until after the final calculation.
Explanation:
In finding the 99% confidence interval about the population mean, one begins by calculating the sample mean (average) and sample standard deviation from the provided data: 51, 73.5, 59.3, 97.3, 67.9, 39.1, and 58.7. The sample mean (x) is obtained by summing the values and dividing by the sample size.
The variance, (s²) used in calculating the standard deviation, is found by taking each number, subtracting the mean, squaring the result, and then averaging these squares. The square root of this result gives the standard deviation (s).
The critical value associated with a 99% confidence level in a normal distribution can be gotten from a standard Z table or Z-distribution table. It is roughly 2.57.
Thereafter, the confidence interval is computed using the formula: x ± (critical value * (s/√n)). Keeping all decimal places in intermediate calculations, only rounding the final answer to two decimal places to prevent rounding errors.
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