Your factorys inventory level was determined at 12 randomly selected times last year, with the following results: 313, 891, 153, 387, 584, 162, 742, 684, 277, 271, 285, 845.

Find the typical inventory level throughout the whole year, using the standard statistical summary.

Identify the population.

Find the 95% confidence interval for the population mean inventory level.

Is the average of the measured inventory levels significantly different from 500, which is the number used for management budgeting purposes? Please find the hypotheses H0 and Ha and justify your answer using a t test.