You are considering the purchase of an expensive passive solar heating device wh
ID: 448172 • Letter: Y
Question
You are considering the purchase of an expensive passive solar heating device which the seller claims will be effective in reducing your monthly home heating expenses. Before you buy this device, you survey 40 randomly selected homes in your area that have already purchased the device. You ask each homeowner what their monthly heating expenses were before they purchased the device and their monthly heating expenses after the solar heating device was installed.
The results are in the following table:
Home #
Mo. Heating Bill Without Passive Solar System ($)
Mo. Heating Bill With Passive Solar System ($)
1
252
248
2
256
262
3
218
236
4
297
309
5
265
236
6
260
259
7
298
299
8
254
252
9
293
285
10
221
199
11
279
266
12
261
264
13
228
218
14
200
219
15
269
249
16
299
283
17
280
251
18
263
273
19
251
251
20
206
223
21
292
301
22
254
244
23
212
187
24
250
256
25
247
238
26
276
293
27
246
222
28
282
267
29
202
194
30
260
243
31
243
261
32
288
284
33
262
266
34
267
261
35
250
240
36
251
256
37
218
220
38
250
243
39
286
257
40
277
267
Assume that the solar heating equipment costs $3,000 to buy and install. Using the appropriate 98% confidence interval, calculate how many years it will take you to "break even" if you make this investment (ignore the Time Value Of Money)
Home #
Mo. Heating Bill Without Passive Solar System ($)
Mo. Heating Bill With Passive Solar System ($)
1
252
248
2
256
262
3
218
236
4
297
309
5
265
236
6
260
259
7
298
299
8
254
252
9
293
285
10
221
199
11
279
266
12
261
264
13
228
218
14
200
219
15
269
249
16
299
283
17
280
251
18
263
273
19
251
251
20
206
223
21
292
301
22
254
244
23
212
187
24
250
256
25
247
238
26
276
293
27
246
222
28
282
267
29
202
194
30
260
243
31
243
261
32
288
284
33
262
266
34
267
261
35
250
240
36
251
256
37
218
220
38
250
243
39
286
257
40
277
267
Explanation / Answer
Below table shows the additional column with the difference in bill after applying the solar heating device.
As we can see above.
Mean = 4.53 , Standard Deviation = 13.87
Now 98% confidence level means z* value = 2.33
Hence at 98% confidence level range of mean will be between
Mean + Z* (Standard Deviation / Square root of sample size) and
Mean - Z* (Standard Deviation / Square root of sample size)
Hence it will be:
[4.53 + 2.33 * (13.87 / Square root (40)) ] and [4.53 - 2.33 * (13.87 / Square root (40)) ]
= 4.53 + 5.11 and 4.53 - 5.11
= Between 9.64 and -0.58
Since this is monthly mean of difference after applying solar heating equipment. The annual range will be between (9.64*12 ) and (-0.58*12) = $115.68 and $-6.96
Now considering best case mean of annual advantage of $115.68 and without taking into account time value of money, the time taken to break even the equipment cost of $3000 will be = 3000/115.68 = 25.93 years
However in worst case since the mean is suggesting that monthly bill is in fact increasing after applying solar equipment so there is a loss and it will never reach the break even.
Home # Mo. Heating Bill Without Passive Solar System ($) Mo. Heating Bill With Passive Solar System ($) Difference after applying solar heater 1 252 248 4 2 256 262 -6 3 218 236 -18 4 297 309 -12 5 265 236 29 6 260 259 1 7 298 299 -1 8 254 252 2 9 293 285 8 10 221 199 22 11 279 266 13 12 261 264 -3 13 228 218 10 14 200 219 -19 15 269 249 20 16 299 283 16 17 280 251 29 18 263 273 -10 19 251 251 0 20 206 223 -17 21 292 301 -9 22 254 244 10 23 212 187 25 24 250 256 -6 25 247 238 9 26 276 293 -17 27 246 222 24 28 282 267 15 29 202 194 8 30 260 243 17 31 243 261 -18 32 288 284 4 33 262 266 -4 34 267 261 6 35 250 240 10 36 251 256 -5 37 218 220 -2 38 250 243 7 39 286 257 29 40 277 267 10 Mean 4.53 Standard Deviation 13.87Related Questions
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