Confidence with 90%, the mean execution time of a job is between 15.17s and 51.89s, while the variance is 56.118s².
Here are the 90% confidence intervals for the mean and the variance of execution time of a job:
Mean: (15.167, 51.899)
Variance: (56.118, 56.118)
To calculate these confidence intervals, we first need to calculate the sample mean and variance. The sample mean is 31.733 seconds and the sample variance is 1095.996 seconds^2.
Next, we need to calculate the standard deviation. The standard deviation is the square root of the variance, which is 33.106 seconds.
Finally, we can calculate the confidence intervals using the following formulas:
Mean confidence interval:
mean ± (z_critical * standard deviation / sqrt(n))
Variance confidence interval:
(n - 1) * variance / chi-square_value
where:
`z_critical` is the z-score that corresponds to the desired confidence level (in this case, 0.90).
`standard deviation` is the standard deviation of the sample.
`n` is the sample size (in this case, 30).
`chi-square_value` is the chi-square value for the desired confidence level and degrees of freedom (in this case, 29 degrees of freedom and a confidence level of 0.90).
The z-critical value for a 90% confidence level is 1.645. The chi-square value for 29 degrees of freedom and a confidence level of 0.90 is 42.557.
Plugging these values into the formulas, we get the following confidence intervals:
Mean confidence interval:
31.733 ± (1.645 * 33.106 / sqrt(30))
(15.167, 51.899)
Variance confidence interval:
(30 - 1) * 1095.996 / 42.557
(56.118, 56.118)
Therefore, we can be 90% confident that the true mean execution time of a job is between 15.17 seconds and 51.89 seconds. We can also be 90% confident that the true variance of execution time of a job is 56.118 seconds^2.