Refer to Example 6.1 and the problem of estimating , the average amount of money owed by

Refer to Example 6.1 and the problem of estimating μ, the average amount of money owed by a bank’s delinquent debtors. The overdue amounts for the n = 100 delinquent accounts are shown in Table 6.1. Use the data to find a 95% confidence interval for μ and interpret the result.

Example 6.1

Consider the large bank that wants to estimate the average amount of money owed by its delinquent debtors, μ. The bank randomly samples n = 100 of its delinquent accounts and finds that the sample mean amount owed is x̄ = $230. Also, suppose it is known that the standard deviation of the amount owed for all delinquent accounts is σ = $90. Use the interval estimator x̄ ± 1.96σ_x̄ to calculate a confidence interval for the target parameter, μ.

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Table 6.1 Overdue Amounts (in Dollars) for 100 Delinquent Accounts 195 209 400 142 312 221 355 293 242 458 278 202 222 334 208 363 146 215 512 209 207 237 371 238 203 162 160 119 328 304 82 368 344 243 162 222 221 193 135 178 259 141 274 132 134 236 449 134 252 180 108 158 278 133 275 178 265 138 365 148 289 240 190 331 17 157 113 206 232 86 330 357 219 229 310 271 234 227 187 77 221 378 194 221 293 121 244 162 364 171 289 148 135 243 310 134 266 354 268 280