Question

Assume that farm sizes in a particular region are normally distributed with a population standard deviation of 150acres. A random sample of 50 farm sizes in this region is given below in acres. Estimate the mean farm size for this region with 90% confidence. Round your answers to two decimal places and use ascending order.

Size

202

1092

1321

319

331

938

73

200

200

229

160

486

370

256

351

770

170

288

177

165

67

194

353

296

293

2179

934

1490

107

79

1756

206

171

1312

188

438

474

131

56

204

1397

162

537

608

171

181

409

175

210

2612

Size

202

1092

1321

319

331

938

73

200

200

229

160

486

370

256

351

770

170

288

177

165

67

194

353

296

293

2179

934

1490

107

79

1756

206

171

1312

188

438

474

131

56

204

1397

162

537

608

171

181

409

175

210

2612

Answer #1

Solution:

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± Z*σ/sqrt(n)

From given data, we have

Xbar = 509.76

σ = 150

n = 50

Confidence level = 90%

Critical Z value = 1.6449

(by using z-table)

Confidence interval = Xbar ± Z*σ/sqrt(n)

Confidence interval = 509.76 ± 1.6449*150/sqrt(50)

Confidence interval = 509.76 ± 1.6449*21.2132

Confidence interval = 509.76 ± 34.8926

Lower limit = 509.76 - 34.8926 = 474.87

Upper limit = 509.76 + 34.8926 = 544.65

Confidence interval = (474.87, 544.65)

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