Question

This data provides 715 observations on variable X1, X2, and X3. Use Excel or MegaStat for the questions below:

a. Conduct the z-test at the 0.05 level to see if the population means for X2 and X3 are equal.

b. Conduct a test at the 0.05 level to see if the variance of X2 and X3 are equal.

c. Test to see whether the variance of X1 is greater than 9. Conduct this test at the 0.05 level.

d. conduct a simple ANOVA test to see whether the means of X1, X2, X3 are equal. Conduct this test at the 0.05 level. How do the means differ?

Observation X1 X2 X3
1 2.82 28.50 142.20
2 2.70 28.60 139.30
3 2.80 28.60 138.40
4 2.95 28.60 139.70
5 2.84 28.70 138.70
6 3.21 28.90 139.40
7 3.20 28.80 140.30
8 3.38 28.90 140.00
9 4.04 28.90 140.40
10 4.05 28.80 140.70
11 4.15 28.80 141.80
12 4.49 28.80 143.60
13 4.35 28.80 143.30
14 3.96 28.80 139.80
15 3.31 28.80 138.50
16 3.23 28.80 139.70
17 3.29 28.80 137.60
18 2.46 28.80 137.90
19 2.30 28.70 138.90
20 2.30 28.70 139.40
21 2.48 28.80 140.50
22 2.30 28.80 141.20
23 2.37 28.80 142.30
24 2.25 28.70 144.50
25 2.24 28.70 144.50
26 2.42 28.70 141.60
27 2.39 28.70 140.60
28 2.29 28.70 142.40
29 2.29 28.70 140.60
30 2.33 28.70 141.20
31 2.24 28.80 141.50
32 2.39 28.90 141.40
33 2.28 29.00 143.10
34 2.30 29.10 144.40
35 2.48 29.20 146.30
36 2.60 29.30 149.20
37 2.72 29.40 148.90
38 2.73 29.50 145.60
39 2.72 29.60 144.60
40 2.73 29.80 146.70
41 2.69 29.80 144.50
42 2.73 29.80 144.80
43 2.92 29.90 145.00
44 2.82 30.00 144.40
45 2.78 30.00 145.50
46 2.74 30.10 147.00
47 2.83 30.20 148.80
48 2.87 30.30 151.90
49 2.91 30.40 152.10
50 2.92 30.60 148.70
51 2.89 30.70 147.80
52 2.90 31.00 150.00
53 2.93 31.00 147.90
54 2.99 31.20 148.70
55 3.18 31.40 149.90
56 3.32 31.50 149.50
57 3.38 31.70 151.00
58 3.45 31.80 152.80
59 3.52 32.00 155.20
60 3.52 32.20 157.50
61 3.52 32.30 157.90
62 3.53 32.40 153.90
63 3.54 32.60 153.10
64 3.47 32.70 155.20
65 3.48 32.90 152.70
66 3.48 33.20 153.90
67 3.46 33.20 155.50
68 3.50 33.40 155.50
69 3.53 33.60 157.80
70 3.57 33.60 159.70
71 3.64 33.80 161.60
72 3.84 33.90 164.90
73 3.81 34.00 165.30
74 3.93 34.20 160.30
75 3.93 34.30 159.90
76 3.93 34.40 162.60
77 3.89 34.50 158.70
78 3.80 34.70 160.50
79 3.84 34.90 161.80
80 3.84 35.10 161.20
81 3.92 35.30 163.90
82 4.03 35.60 166.50
83 4.09 35.80 168.20
84 4.38 36.00 172.60
85 4.59 36.20 173.80
86 4.65 36.40 168.60
87 4.59 36.50 168.70
88 4.62 36.70 172.40
89 4.64 37.00 168.00
90 4.50 37.00 170.00
91 4.80 37.20 169.20
92 4.96 37.40 168.30
93 5.37 37.50 171.10
94 5.35 37.70 171.60
95 5.32 37.80 172.90
96 4.96 38.00 176.90
97 4.72 38.20 176.60
98 4.56 38.40 171.60
99 4.26 38.50 172.90
100 3.84 38.60 174.70
101 3.60 38.80 172.30
102 3.54 38.90 175.60
103 4.21 39.00 177.20
104 4.27 39.20 177.20
105 4.42 39.40 179.80
106 4.56 39.60 181.90
107 4.73 39.70 183.80
108 4.97 40.00 188.40
109 5.00 40.50 189.20
110 4.98 40.30 183.00
111 5.17 40.60 183.50
112 5.38 40.90 187.30
113 5.66 41.00 184.60
114 5.52 41.40 188.20
115 5.31 41.60 189.80
116 5.09 41.80 189.50
117 5.19 42.20 191.90
118 5.35 42.40 194.20
119 5.45 42.70 197.60
120 5.96 43.00 202.80
121 6.14 43.10 203.80
122 6.12 43.40 197.30
123 6.02 43.60 197.80
124 6.11 43.80 201.50
125 6.04 43.90 197.40
126 6.44 44.20 200.20
127 7.00 44.50 201.20
128 6.98 44.70 199.50
129 7.09 44.90 201.20
130 7.00 45.20 202.90
131 7.24 45.50 205.00
132 7.82 45.70 209.30
133 7.87 46.00 210.80
134 7.13 46.10 202.00
135 6.63 46.30 203.50
136 6.51 46.50 208.10
137 6.84 46.90 204.30
138 6.68 47.20 206.90
139 6.45 47.40 208.10
140 6.41 47.60 208.00
141 6.12 47.90 210.80
142 5.91 48.10 212.30
143 5.28 48.30 214.50
144 4.87 48.60 220.10
145 4.44 48.90 220.40
146 3.70 49.20 214.30
147 3.38 49.40 216.40
148 3.86 49.70 221.40
149 4.14 50.00 218.80
150 4.75 50.40 222.90
151 5.40 50.90 225.10
152 4.94 51.20 223.60
153 4.69 51.40 225.40
154 4.46 51.60 226.60
155 4.22 51.80 228.80
156 4.01 52.00 234.50
157 3.38 52.30 235.00
158 3.20 52.60 228.90
159 3.73 53.00 231.70
160 3.71 53.10 236.90
161 3.69 53.40 232.20
162 3.91 53.70 236.10
163 3.98 54.00 239.10
164 4.02 54.40 238.70
165 4.66 54.80 241.90
166 4.74 55.30 244.20
167 4.78 55.70 247.70
168 5.07 56.20 256.10
169 5.41 56.60 256.40
170 5.60 56.90 248.40
171 6.09 57.20 248.80
172 6.26 57.80 254.00
173 6.36 58.10 250.80
174 7.19 58.50 256.40
175 8.01 58.80 258.10
176 8.67 59.10 255.60
177 8.29 59.60 256.50
178 7.22 59.90 258.30
179 7.83 60.30 262.70
180 7.45 60.80 270.20
181 7.77 61.30 268.60
182 7.12 61.80 261.10
183 7.96 62.30 263.50
184 8.33 63.00 268.50
185 8.23 63.40 263.30
186 7.90 63.70 268.30
187 7.55 64.10 270.10
188 8.96 64.70 268.10
189 8.06 65.20 269.70
190 7.46 65.80 271.70
191 7.47 66.50 275.70
192 7.15 67.00 281.80
193 6.26 67.40 278.50
194 5.50 67.80 269.90
195 5.49 68.40 272.90
196 5.61 68.50 277.70
197 5.23 69.10 274.40
198 5.34 70.00 282.30
199 6.13 70.50 284.40
200 6.44 71.00 282.70
201 6.42 71.20 284.30
202 5.96 71.70 284.90
203 5.48 72.30 289.90
204 5.44 72.80 295.30
205 4.87 73.20 293.20
206 4.88 73.90 285.30
207 5.00 74.70 287.70
208 4.86 75.50 296.10
209 5.20 76.10 291.30
210 5.41 76.60 295.60
211 5.23 77.10 298.40
212 5.14 77.60 297.10
213 5.08 78.10 298.60
214 4.92 78.60 302.90
215 4.75 79.10 305.70
216 4.35 79.50 314.50
217 4.62 80.20 313.60
218 4.67 80.80 304.90
219 4.60 81.30 308.20
220 4.54 82.10 318.60
221 4.96 82.50 311.60
222 5.02 83.10 317.70
223 5.19 83.90 322.20
224 5.49 84.50 320.20
225 5.81 85.20 323.70
226 6.16 85.90 327.90
227 6.10 86.60 331.40
228 6.07 87.40 340.00
229 6.44 88.00 339.30
230 6.45 88.70 327.90
231 6.29 89.40 330.80
232 6.29 90.00 343.40
233 6.41 90.80 338.20
234 6.73 91.50 345.20
235 7.01 92.00 349.50
236 7.08 92.70 347.50
237 7.85 93.60 352.70
238 7.99 94.40 354.90
239 8.64 95.20 358.50
240 9.08 96.00 367.90
241 9.35 96.80 363.30
242 9.32 97.40 351.70
243 9.48 98.00 356.10
244 9.46 98.80 371.30
245 9.61 99.50 362.20
246 9.06 100.30 371.90
247 9.24 101.20 378.40
248 9.52 102.10 376.90
249 10.26 103.10 380.50
250 11.70 103.90 382.60
251 11.79 104.30 384.40
252 12.04 104.80 393.20
253 12.00 106.00 390.40
254 12.86 106.70 380.80
255 15.20 107.50 382.20
256 13.20 107.70 386.70
257 8.58 108.70 377.80
258 7.07 109.60 387.30
259 8.06 110.50 394.60
260 9.13 111.70 398.30
261 10.27 112.40 404.70
262 11.62 113.40 410.70
263 13.73 114.90 415.80
264 15.49 115.30 419.50
265 15.02 115.30 416.40
266 14.79 116.20 405.50
267 13.36 117.00 412.20
268 13.69 117.90 431.00
269 16.30 118.30 418.50
270 14.73 118.70 422.80
271 14.95 119.50 427.70
272 15.51 119.90 425.90
273 14.70 120.10 427.00
274 13.54 120.50 429.70
275 10.86 121.40 435.10
276 10.85 122.50 447.00
277 12.28 123.20 448.40
278 13.48 123.90 432.40
279 12.68 124.40 435.60
280 12.70 125.50 451.10
281 12.09 126.70 440.90
282 12.47 127.40 446.20
283 11.35 128.10 449.50
284 8.68 129.00 449.80
285 7.92 129.90 456.20
286 7.71 130.90 465.70
287 8.07 131.60 474.40
288 7.94 132.50 485.80
289 7.86 133.60 482.80
290 8.11 135.00 474.20
291 8.35 136.40 482.70
292 8.21 137.40 498.60
293 8.19 138.70 493.90
294 8.79 139.60 503.50
295 9.08 140.60 510.50
296 9.34 141.40 508.20
297 9.00 142.70 511.40
298 8.64 144.10 517.20
299 8.76 145.30 521.80
300 9.00 146.20 533.30
301 8.90 147.40 530.20
302 9.09 148.00 516.90
303 9.52 149.10 523.20
304 9.69 150.10 539.90
305 9.83 150.70 530.70
306 9.87 151.90 541.40
307 10.12 152.70 543.30
308 10.47 153.50 539.00
309 10.37 154.40 542.50
310 9.74 154.70 542.20
311 8.61 155.50 549.80
312 8.06 156.10 564.60
313 7.76 156.80 561.10
314 8.27 157.90 551.90
315 8.52 158.50 558.40
316 7.95 159.30 575.10
317 7.48 160.40 569.30
318 6.95 161.70 585.20
319 7.08 162.80 592.00
320 7.14 164.20 594.90
321 7.10 165.10 602.00
322 7.16 166.10 605.30
323 7.24 167.00 614.90
324 7.10 167.70 633.30
325 7.07 168.40 626.60
326 7.06 169.40 612.80
327 6.56 170.70 624.30
328 6.06 171.40 647.00
329 6.15 172.70 645.70
330 6.21 173.60 662.80
331 5.83 174.70 673.40
332 5.53 175.90 678.40
333 5.21 176.80 684.50
334 5.18 178.20 692.20
335 5.35 179.20 708.80
336 5.53 180.40 739.80
337 5.43 181.90 737.10
338 5.59 183.30 717.10
339 5.59 184.00 723.10
340 5.64 185.30 752.00
341 5.66 186.50 739.30
342 5.67 187.60 743.80
343 5.69 188.70 746.20
344 6.04 190.00 744.20
345 6.40 191.40 744.50
346 6.13 193.10 753.20
347 5.69 195.20 755.50
348 5.77 196.70 765.40
349 5.81 197.90 764.20
350 5.66 198.90 744.50
351 5.70 200.20 751.60
352 5.91 201.80 777.90
353 6.26 203.20 763.40
354 6.46 204.60 778.50
355 6.73 206.10 785.50
356 7.06 207.10 781.00
357 7.24 208.60 779.70
358 7.35 209.70 780.80
359 7.76 210.70 786.90
360 8.07 212.00 803.10
361 8.27 212.90 792.10
362 8.53 213.50 771.60
363 8.82 214.70 774.60
364 8.65 215.30 790.20
365 8.43 216.30 766.10
366 8.15 217.20 772.80
367 7.88 218.00 780.70
368 7.90 218.50 776.50
369 7.75 219.10 777.70
370 7.64 219.80 783.20
371 7.69 220.50 790.20
372 7.63 222.30 810.60
373 7.64 223.90 800.70
374 7.74 225.50 786.70
375 7.90 227.50 794.50
376 7.77 229.40 816.20
377 7.74 231.20 795.50
378 7.73 233.30 809.00
379 7.62 235.50 811.00
380 7.45 238.40 812.70
381 7.36 241.40 817.10
382 7.17 243.50 816.10
383 7.06 245.00 824.60
384 6.74 246.50 842.70
385 6.22 250.60 831.70
386 5.94 253.50 822.10
387 5.91 255.70 833.70
388 5.65 255.70 851.90
389 5.46 256.50 840.30
390 5.57 257.60 856.70
391 5.58 259.10 860.90
392 5.33 260.90 863.20
393 5.22 262.10 865.40
394 4.99 263.70 874.00
395 4.56 265.50 892.30
396 4.07 267.10 915.60
397 3.80 268.60 916.40
398 3.84 270.20 915.10
399 4.04 271.50 929.60
400 3.75 273.10 953.70
401 3.63 274.80 942.90
402 3.66 276.30 951.00
403 3.21 279.20 962.00
404 3.13 282.00 970.10
405 2.91 284.90 982.70
406 2.86 287.30 1000.80
407 3.13 289.50 1021.40
408 3.22 292.10 1045.60
409 3.00 294.20 1039.80
410 2.93 296.10 1021.90
411 2.95 298.30 1030.50
412 2.87 301.00 1057.40
413 2.96 303.80 1056.80
414 3.07 306.40 1071.80
415 3.04 309.40 1083.10
416 3.02 311.90 1088.10
417 2.95 314.90 1098.80
418 3.02 317.30 1111.60
419 3.10 319.10 1129.00
420 3.06 321.60 1153.30
421 2.98 324.90 1141.70
422 3.25 328.10 1123.80
423 3.50 331.10 1131.10
424 3.68 333.70 1152.20
425 4.14 336.80 1132.00
426 4.14 339.80 1141.80
427 4.33 343.60 1150.90
428 4.48 345.40 1144.10
429 4.62 347.70 1146.40
430 4.95 350.30 1147.90
431 5.29 353.00 1156.20
432 5.60 354.50 1174.50
433 5.71 357.40 1159.50
434 5.77 358.50 1135.30
435 5.73 362.20 1139.30
436 5.65 365.50 1160.30
437 5.67 368.00 1134.00
438 5.47 367.90 1141.00
439 5.42 368.20 1145.70
440 5.40 368.80 1139.30
441 5.28 369.80 1138.40
442 5.28 370.90 1132.90
443 5.36 371.50 1138.60
444 5.14 372.80 1152.70
445 5.00 373.30 1130.20
446 4.83 372.40 1105.80
447 4.96 374.90 1118.00
448 4.95 376.10 1131.80
449 5.02 377.70 1105.90
450 5.09 380.20 1115.00
451 5.15 383.10 1110.70
452 5.05 385.70 1097.70
453 5.09 387.90 1091.70
454 4.99 389.90 1078.40
455 5.03 392.20 1087.40
456 4.91 394.60 1105.80
457 5.03 396.80 1087.90
458 5.01 398.80 1066.80
459 5.14 401.50 1069.20
460 5.16 403.30 1074.50
461 5.05 406.20 1054.70
462 4.93 408.50 1064.80
463 5.05 410.80 1065.80
464 5.14 413.20 1069.10
465 4.95 415.60 1059.50
466 4.97 418.20 1057.60
467 5.14 421.80 1074.10
468 5.16 425.30 1097.50
469 5.04 427.50 1080.20
470 5.09 430.00 1066.20
471 5.03 431.90 1075.90
472 4.95 433.80 1087.70
473 5.00 436.10 1070.80
474 4.98 438.70 1075.20
475 4.96 442.20 1074.20
476 4.90 444.80 1069.30
477 4.61 449.80 1070.60
478 3.96 453.70 1077.40
479 4.41 457.20 1098.00
480 4.39 460.40 1121.20
481 4.34 463.40 1103.90
482 4.44 467.40 1085.20
483 4.44 471.60 1097.50
484 4.29 475.70 1113.60
485 4.50 480.00 1096.40
486 4.57 483.40 1098.20
487 4.55 487.10 1097.20
488 4.72 490.50 1092.80
489 4.68 494.50 1086.20
490 4.86 499.20 1095.10
491 5.07 505.30 1113.00
492 5.20 517.90 1148.20
493 5.32 524.90 1126.90
494 5.55 518.00 1097.40
495 5.69 516.90 1108.90
496 5.66 517.90 1125.70
497 5.79 519.10 1100.40
498 5.69 521.20 1101.80
499 5.96 522.60 1102.80
500 6.09 522.80 1094.50
501 6.00 524.10 1088.80
502 6.11 526.20 1092.20
503 6.17 528.30 1092.10
504 5.77 531.30 1111.70
505 5.15 534.10 1100.40
506 4.88 536.70 1089.80
507 4.42 539.30 1111.20
508 3.87 542.70 1126.70
509 3.62 545.80 1114.70
510 3.49 548.70 1126.30
511 3.51 554.40 1139.70
512 3.36 562.40 1144.50
513 2.64 567.80 1193.60
514 2.16 571.60 1159.20
515 1.87 575.80 1169.00
516 1.69 581.20 1208.50
517 1.65 586.60 1191.80
518 1.72 591.30 1178.30
519 1.79 595.40 1196.80
520 1.71 599.50 1196.90
521 1.73 604.90 1186.00
522 1.70 610.20 1194.70
523 1.68 615.40 1200.40
524 1.62 616.90 1182.30
525 1.63 618.20 1185.80
526 1.58 620.00 1196.60
527 1.23 622.80 1205.30
528 1.19 626.20 1245.50
529 1.17 630.10 1225.50
530 1.17 635.00 1225.50
531 1.13 639.40 1245.10
532 1.13 643.00 1259.60
533 1.07 645.80 1266.60
534 0.92 647.40 1284.70
535 0.90 648.30 1287.90
536 0.95 650.20 1292.20
537 0.94 652.70 1286.20
538 0.92 657.40 1288.80
539 0.93 660.00 1293.90
540 0.90 662.50 1332.50
541 0.88 663.80 1301.80
542 0.93 665.40 1306.70
543 0.94 666.90 1337.90
544 0.94 669.80 1343.20
545 1.02 673.10 1333.40
546 1.27 677.60 1347.70
547 1.33 685.40 1338.80
548 1.48 686.80 1352.60
549 1.65 690.40 1349.10
550 1.76 693.50 1351.40
551 2.07 697.80 1371.00
552 2.19 697.80 1401.50
553 2.33 698.90 1361.50
554 2.54 700.40 1355.00
555 2.74 702.00 1381.70
556 2.78 703.40 1369.40
557 2.84 704.60 1369.50
558 2.97 708.20 1384.30
559 3.22 710.60 1365.40
560 3.44 713.40 1376.90
561 3.42 717.20 1363.50
562 3.71 718.40 1365.40
563 3.88 720.60 1373.60
564 3.89 724.60 1397.20
565 4.24 729.30 1375.50
566 4.43 733.20 1362.00
567 4.51 735.60 1394.70
568 4.60 738.20 1393.60
569 4.72 741.30 1392.10
570 4.79 740.80 1379.00
571 4.95 740.80 1368.60
572 4.96 742.10 1370.60
573 4.81 742.60 1347.40
574 4.92 743.70 1360.30
575 4.94 746.60 1368.50
576 4.85 750.20 1387.70
577 4.98 750.70 1369.00
578 5.03 750.00 1347.50
579 4.94 750.80 1378.40
580 4.87 753.70 1392.30
581 4.73 755.30 1385.60
582 4.61 755.70 1370.80
583 4.82 758.10 1368.60
584 4.20 759.00 1372.80
585 3.89 760.20 1356.30
586 3.90 762.90 1369.40
587 3.27 762.70 1370.50
588 3.00 760.60 1394.90
589 2.75 758.30 1375.90
590 2.12 757.40 1365.90
591 1.26 759.20 1401.10
592 1.29 758.20 1406.60
593 1.73 762.40 1396.50
594 1.86 768.50 1407.30
595 1.63 774.80 1417.70
596 1.72 776.80 1401.30
597 1.13 780.90 1441.50
598 0.67 796.70 1462.60
599 0.19 806.40 1513.70
600 0.03 816.20 1632.30
601 0.13 829.50 1580.70
602 0.30 837.60 1552.00
603 0.21 843.00 1594.90
604 0.16 847.20 1627.70
605 0.18 848.60 1617.90
606 0.18 852.30 1661.70
607 0.18 854.80 1657.70
608 0.17 858.30 1651.30
609 0.12 861.40 1641.00
610 0.07 862.80 1664.30
611 0.05 862.00 1683.10
612 0.05 863.70 1724.40
613 0.06 864.50 1674.20
614 0.11 868.40 1685.20
615 0.15 871.60 1729.50
616 0.16 876.00 1716.00
617 0.16 879.90 1708.20
618 0.12 882.90 1732.30
619 0.16 887.40 1718.40
620 0.16 893.10 1739.60
621 0.15 899.40 1741.40
622 0.13 907.40 1767.40
623 0.14 915.00 1828.70
624 0.14 918.80 1871.40
625 0.15 923.30 1855.60
626 0.13 930.20 1858.70
627 0.10 938.00 1909.40
628 0.06 947.70 1918.00
629 0.04 956.80 1934.20
630 0.04 963.70 1954.10
631 0.04 969.70 1994.50
632 0.02 976.50 2101.90
633 0.01 982.40 2099.10
634 0.02 986.30 2128.10
635 0.01 994.80 2164.40
636 0.01 1001.60 2208.10
637 0.03 1009.90 2209.20
638 0.09 1019.50 2194.50
639 0.08 1028.40 2246.00
640 0.08 1034.30 2268.60
641 0.09 1039.60 2248.40
642 0.09 1046.20 2271.00
643 0.10 1052.30 2314.60
644 0.10 1059.40 2334.60
645 0.11 1068.10 2358.00
646 0.10 1077.00 2416.20
647 0.09 1083.60 2415.20
648 0.07 1090.70 2509.70
649 0.07 1097.20 2481.30
650 0.10 1100.00 2455.70
651 0.09 1103.90 2497.20
652 0.06 1109.30 2542.30
653 0.04 1116.40 2518.50
654 0.05 1123.10 2523.50
655 0.04 1131.00 2543.70
656 0.04 1137.70 2537.40
657 0.02 1145.00 2555.80
658 0.05 1151.40 2618.40
659 0.07 1154.50 2607.20
660 0.07 1160.70 2715.70
661 0.04 1165.70 2701.70
662 0.05 1171.90 2706.20
663 0.05 1189.70 2773.30
664 0.03 1198.30 2809.60
665 0.03 1205.00 2782.20
666 0.04 1211.90 2824.80
667 0.03 1218.40 2841.20
668 0.03 1223.60 2790.20
669 0.02 1227.60 2834.60
670 0.02 1231.70 2865.00
671 0.02 1241.50 2861.10
672 0.03 1253.30 2992.00
673 0.03 1266.70 2941.10
674 0.02 1273.00 2979.60
675 0.03 1279.30 3023.90
676 0.02 1284.60 3035.40
677 0.02 1288.80 2975.90
678 0.02 1294.30 3020.70
679 0.03 1301.10 3038.40
680 0.07 1309.30 3022.30
681 0.02 1318.10 3016.30
682 0.02 1325.20 3011.90
683 0.12 1333.90 3056.20
684 0.23 1339.60 3141.10
685 0.26 1346.30 3094.30
686 0.31 1352.30 3097.40
687 0.29 1359.80 3181.20
688 0.23 1366.00 3236.50
689 0.27 1374.50 3237.30
690 0.27 1381.60 3250.10
691 0.30 1388.20 3248.40
692 0.30 1395.10 3322.60
693 0.29 1401.00 3300.50
694 0.33 1407.50 3330.40
695 0.45 1415.30 3327.00
696 0.51 1421.30 3382.80
697 0.51 1431.90 3387.70
698 0.52 1434.80 3346.50
699 0.74 1446.70 3467.50
700 0.80 1457.60 3473.20
701 0.89 1467.60 3503.60
702 0.98 1477.00 3508.50
703 1.07 1485.40 3539.30
704 1.01 1493.80 3574.60
705 1.03 1503.20 3533.30
706 1.07 1512.30 3588.60
707 1.23 1518.10 3584.60
708 1.32 1525.80 3636.90
709 1.41 1538.20 3636.30
710 1.57 1540.20 3558.70
711 1.70 1548.70 3686.50
712 1.76 1558.00 3693.30
713 1.86 1569.00 3657.30
714 1.90 1580.30 3660.80
715 1.96 1589.80 3680.40

Answer 1

Using excel,

a. Z test

H₀ : Vs H_a :

The output is obtained as:

Since the p value obtained for the test is 0.00 < 0.05.There is no sufficient evidence to support the null hypothesis.Hence, the null hypothesis may be rejected at 5% level of significance.

We may conclude that the population means for X2 and X3 are not equal.

b.F test for equality of variance of X2 and X3

H₀:   

Since the p value obtained for the test is 0.00 < 0.05.There is no sufficient evidence to support the null hypothesis.Hence, the null hypothesis may be rejected at 5% level of significance.

We may conclude that the population variances for X2 and X3 are not equal.

c To test whether the variance of X1 is greater than 9.

H₀ : vs H_a :

The appropriate test, here, would be chi square.Its test statistic is given by,

Here, s² = Sample variance = 9.911 ............[=VAR(A2:A716) in excel]

= 9..........(given)

n = no. of observations = 715

Substituting the above values,

=786.3

p value for the test is obtained by the formula, CHIDIST(786.3,714) = 0.031 < 0.05

Since the p value obtained for the test is 0.031 < 0.05.There is no sufficient evidence to support the null hypothesis.Hence, the null hypothesis may be rejected at 5% level of significance.

We may conclude that the population variance of X1 is greater than 9.

d. ANOVA to test equality of means of X1,X2 and X3

H₀ : vs H₁: At least one of the means differ.

The output is obtained as:

Since the p value obtained for the test is 0.000 < 0.05.There is no sufficient evidence to support the null hypothesis.Hence, the null hypothesis may be rejected at 5% level of significance.

We may conclude that the population means of X1, X2 and X3 are not equal.The means differ significantly at 5% level.