The numbers of faculty at 32 randomly selected state-controlled colleges and universities with enrolment under 12,000 students are shown below. Use these data to estimate the mean number of faculty at all state-controlled colleges and universities with enrolment under 12,000 with 92% confidence. Assume .

211, 384, 396, 211, 224, 337, 395, 121, 356, 621, 367, 408, 515, 280, 289, 180, 431, 176, 318, 836, 203, 374, 224, 121, 412, 134, 539, 471, 638, 425, 159, 324