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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=165.2211 384 396 211 224 337 395 121 356621 367 408 515 280 289 180 431 176318 836 203 374 224 121 412 134 539471 638 425 159 324

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

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Step 1

Confidence interval:

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

2 Vn
2 Vn
2 Vn
바투
바를 이들
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2 Vn 2 Vn 2 Vn 바투 바를 이들

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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:

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 425159 324
32
11,080
32
346.25
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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 425159 324 32 11,080 32 346.25

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Step 3

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

165.2
σ
- 346.25 t1.75 x
32
2 Vn
=(346.25 51.106)
(295.144,397.356)
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165.2 σ - 346.25 t1.75 x 32 2 Vn =(346.25 51.106) (295.144,397.356)

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