Question

The numbers of faculty at 32 randomly selected state-controlled colleges and universities with enrollment under 12,000 students are shown below. Use the data to estimate the mean number of faculty at all state-controlled colleges and universities with enrollment under 12,000 with 92% confidence. Assume o=165.2

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

Step 1

**Confidence interval:**

The (1-α) % confidence interval for population mean *µ, *when σ is known is given by:

Step 2

**Computing the confidence interval for population mean:**

The number of faculties at 32 randomly selected state-controlled colleges and universities with enrolment under 12,000 students are given. That is, *n=*32. The population standard deviation is 165.2. That is, σ = 165.2. The confidence level is 92%. Therefore, the significance level, α = 0.08.

From the EXCEL, using the formula, = NORM.INV(0.96,0,1), the critical value is 1.75.

The sample mean is given by:

Step 3

Therefore the 92% confidence interval of the mean...

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