Final answer:
To calculate the margin of error E for a 99% confidence level with a sample size of 15 and a sample standard deviation of 5.7, the t-value for 14 degrees of freedom needs to be known. Once obtained, E can be estimated using the formula E = t-value multiplied by (5.7 divided by the square root of 15).
Step-by-step explanation:
To find the value of E, the margin of error, for a given confidence level, sample size, and sample standard deviation, you need to use the formula for the margin of error for a t-distribution, as follows: E = t⁺ × (s / √n).
To compute E for c = 0.99, n = 15, and s = 5.7, you need to find the critical value t⁺ that corresponds to the 0.99 confidence level with 14 degrees of freedom (n - 1 for a sample size of 15). This critical value can be found in a t-distribution table or by using statistical software.
Assuming you have the correct t-value, you would then calculate E as follows: E = t⁺ × (5.7 / √15).
Without the specific t-value, we cannot calculate the exact margin of error E. However, generally, for a 0.99 confidence level and 14 degrees of freedom, the t-value is approximately 2.62.
Thus, E would be approximately 2.62 × (5.7 / √15), but this should be verified with the correct t-value.