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# Null Hypothesis

Can you tell me how you would do the attached problem? My idea is to take the difference of Day 0 and Day 365 (using the absolute value of it) then use ANOVA. Does that make sense?

#### Solution Summary

Please evaluate the following null hypothesis, and apply the principles of statistical inference as appropriate. The data in this project are composite "heart scores" compiled on Day 0 and Day 365 from individuals divided into 4 groups:

Group A: low sodium/low potassium diet
Group B: high sodium/low potassium diet
Group C: low sodium/high potassium diet
Group D: high sodium/high potassium diet

A heart score greater than 8 indicates the existence of serious coronary artery disease.

Ho: heart score is not affected by the ratio of sodium to potassium in the diet
(assume alpha = 0.05)

Group A
subject Day 0 Day 365
1 8.5 6.6
2 0.7 6.7
3 9.6 7.3
4 4.9 5.1
5 9.7 1.8
6 9.0 1.2
7 2.8 3.9
8 2.5 4.1
9 2.8 6.4
10 8.4 6.2
11 4.1 2.7
12 6.7 8.6
13 7.2 6.6
14 9.2 4.1
15 2.9 6.8
16 7.4 4.6
17 0.3 4.0
18 7.5 7.8
19 0.9 2.4
20 7.5 5.5
21 2.1 3.3
22 6.5 4.8
23 8.4 4.8
24 4.6 5.0
25 5.9 7.3
26 3.1 3.2
27 8.2 9.7
28 1.8 1.1
29 3.2 8.3
30 5.9 4.2
31 5.8 8.9
32 6.1 4.2
33 1.8 2.7
34 1.1 5.7
35 8.5 9.8
36 6.6 9.4
37 5.3 4.8
38 1.4 9.6
39 3.7 9.6
40 8.5 1.6
41 6.6 7.6
42 5.3 5.9
43 1.4 5.5
44 3.7 6.8
45 8.5 1.3
46 6.6 5.6
47 5.3 1.3
48 1.4 1.7
49 3.7 6.4
50 8.5 6.1
51 5.2 5.3
52 4.2 6.7
53 2.6 2.4
54 9.5 5.2
55 3.9 5.3
56 4.1 8.9
57 5.4 7.4
58 8.9 4.1
59 3.6 6.9
60 9.8 9.0
61 6.7 2.1
62 8.3 7.6
63 8.3 7.6
64 7.4 5.6
65 6.6 4.5
66 7.4 9.1
67 9.9 8.4
68 5.4 5.0
69 8.5 1.2
70 2.5 4.7
71 5.9 5.8
72 3.4 1.5
73 6.6 9.2
74 7.9 6.0
75 8.7 6.1
76 2.0 8.9
77 8.6 7.2
78 8.5 9.7
79 6.1 3.1
80 0.7 3.5
81 3.3 8.2
82 2.6 7.6
83 8.0 7.3
84 7.9 3.2
85 4.7 8.5
86 1.6 8.2
87 6.6 8.9
88 5.0 1.1
89 1.5 8.6
90 8.8 4.2
91 8.9 9.4
92 0.5 8.8
93 1.4 9.2
94 6.5 6.3
95 5.1 3.1
96 2.1 3.6
97 7.2 1.9
98 0.9 1.7
99 7.0 2.2
100 6.6 4.5
101 6.9 1.0
102 4.4 7.8
103 4.0 6.4
104 8.9 5.1
105 1.3 6.4
106 9.2 4.1
107 8.4 5.5
108 4.2 2.2
109 5.1 8.1
110 5.9 4.9

Group B
subject Day 0 Day 365

111 4.2 3.7
112 6.8 8.6
113 7.3 6.6
114 9.2 5.1
115 2.9 6.8
116 7.5 5.6
117 0.4 5.0
118 7.6 7.8
119 0.9 3.4
120 7.6 6.5
121 2.2 4.3
122 6.6 5.8
123 8.5 5.8
124 4.7 6.0
125 5.9 8.3
126 3.2 4.2
127 8.3 9.7
128 1.8 2.1
129 3.3 8.3
130 5.9 5.2
131 5.8 8.9
132 6.2 5.2
133 1.8 3.7
134 1.2 6.7
135 8.6 9.8
136 6.7 9.4
137 5.4 5.8
138 1.5 9.6
139 3.8 9.6
140 8.6 2.6
141 6.7 8.6
142 5.4 6.9
143 1.5 6.5
144 3.8 7.8
145 8.6 2.3
146 6.7 6.6
147 5.4 3.3
148 1.5 2.7
149 3.7 7.4
150 8.6 7.1
151 5.3 6.3
152 4.3 7.7
153 2.7 3.4
154 9.6 6.2
155 3.9 6.3
156 4.2 8.9
157 5.5 8.4
158 8.9 5.1
159 3.7 7.9
160 9.8 9.0
161 6.8 3.1
162 8.4 8.6
163 8.4 8.6
164 7.5 6.6
165 6.7 5.5
166 7.5 9.1
167 9.9 8.4
168 5.5 6.0
169 8.6 2.2
170 2.6 5.7
171 5.9 6.8
172 3.5 2.5
173 6.7 9.2
174 7.9 7.0
175 8.7 7.1
176 2.3 9.9
177 8.6 8.2
178 8.6 9.7
179 6.2 4.1
180 0.9 4.5
181 3.5 9.2
182 2.6 8.6
183 8.4 8.3
184 7.9 3.2
185 4.7 8.5
186 1.7 9.2
187 6.6 9.9
188 5.3 2.1
189 1.4 9.6
190 8.8 5.2
191 8.9 9.4
192 0.6 7.8
193 1.5 9.2
194 6.8 5.3
195 5.4 4.1
196 2.3 4.6
197 7.5 2.9
198 0.9 2.7
199 7.0 3.2
200 6.3 5.5

Group C
subject Day 0 Day 365
201 7.5 6.6
202 1.7 6.7
203 8.6 6.3
204 5.9 5.1
205 9.7 1.8
206 8.0 2.2
207 3.8 3.9
208 3.5 4.1
209 3.8 5.4
210 7.4 6.2
211 5.1 2.7
212 7.7 7.6
213 8.2 6.6
214 9.2 4.1
215 3.9 5.8
216 6.4 4.6
217 1.3 4.0
218 6.5 6.8
219 1.9 2.4
220 6.5 5.5
221 3.1 4.3
222 5.5 4.8
223 7.4 4.8
224 5.6 5.0
225 6.9 7.3
226 4.1 3.2
227 7.2 8.7
228 2.8 1.1
229 4.2 8.3
230 5.9 5.2
231 5.8 8.9
232 5.1 4.2
233 2.8 3.7
234 2.1 5.7
235 7.5 9.8
236 5.6 8.4
237 5.3 4.8
238 2.4 9.6
239 4.7 8.6
240 7.5 1.6
241 5.6 7.6
242 5.3 5.9
243 2.4 5.5
244 4.7 6.8
245 7.5 4.3
246 5.6 6.6
247 5.3 3.3
248 2.4 2.7
249 4.7 7.4
250 7.5 6.1
251 5.2 5.3
252 5.2 7.7
253 3.6 2.4
254 8.5 5.2
255 4.9 6.3
256 5.1 8.9
257 5.4 7.4
258 7.9 4.1
259 4.6 6.9
260 8.8 9.0
261 5.7 3.1
262 7.3 7.6
263 7.3 7.6
264 7.4 5.6
265 5.6 4.5
266 6.4 9.1
267 8.9 8.4
268 5.4 5.0
269 7.5 2.2
270 3.5 4.7
271 5.9 5.8
272 4.4 1.5
273 5.6 8.2
274 6.9 5.0
275 7.7 5.1
276 3.0 7.9
277 7.6 6.2
278 6.5 8.7
279 6.1 4.1
280 1.7 4.5
281 4.3 7.2
282 3.6 6.6
283 7.0 6.3
284 6.9 4.2
285 5.7 7.5
286 2.6 7.2
287 5.6 7.9
288 5.0 2.1
289 2.5 7.6
290 7.8 5.2
291 7.9 8.4
292 1.5 7.8
293 2.4 8.2
294 5.5 5.3
295 5.1 4.1
296 3.1 4.6
297 6.2 2.9
298 1.9 2.7
299 6.0 3.2
300 5.6 5.5

Group D
subject Day 0 Day 365

301 6.9 2.0
302 4.4 7.8
303 4.0 5.4
304 8.9 5.1
305 1.3 5.4
306 9.2 4.1
307 8.4 5.5
308 4.2 2.2
309 5.1 7.1
310 5.9 4.9
311 4.2 4.7
312 6.8 8.6
313 7.3 5.6
314 9.2 5.1
315 2.9 5.8
316 7.5 5.6
317 0.4 5.0
318 7.6 7.8
319 0.9 4.4
320 7.6 6.5
321 2.2 5.3
322 6.6 5.8
323 8.5 5.8
324 4.7 6.0
325 5.9 7.3
326 3.2 4.2
327 8.3 8.7
328 1.8 2.1
329 3.3 8.3
330 5.9 5.2
331 5.8 7.9
332 6.2 5.2
333 1.8 4.7
334 1.2 6.7
335 8.6 8.8
336 6.7 9.4
337 5.4 5.8
338 1.5 8.6
339 3.8 8.6
340 8.6 2.6
341 6.7 7.6
342 5.4 6.9
343 1.5 5.5
344 3.8 7.8
345 8.6 3.3
346 6.7 6.6
347 5.4 4.3
348 1.5 2.7
349 3.7 6.4
350 8.6 7.1
351 5.3 5.3
352 4.3 7.7
353 2.7 4.4
354 9.6 6.2
355 3.9 5.3
356 4.2 8.9
357 5.5 7.4
358 8.9 5.1
359 3.7 6.9
360 9.8 9.0
361 6.8 4.1
362 8.4 8.6
363 8.4 7.6
364 7.5 6.6
365 6.7 5.5
366 7.5 9.1
367 9.9 7.4
368 5.5 6.0
369 8.6 3.2
370 2.6 5.7
371 5.9 5.8
372 3.5 2.5
373 6.7 8.2
374 7.9 7.0
375 8.7 6.1
376 2.3 9.9
377 8.6 7.2
378 8.6 9.7
379 6.2 5.1
380 0.9 4.5
381 3.5 8.2
382 2.6 8.6
383 8.4 7.3
384 7.9 3.2
385 4.7 7.5
386 1.7 9.2
387 6.6 8.9
388 5.3 2.1
389 1.4 8.6
390 8.8 5.2
391 8.9 8.4
392 0.6 7.8
393 1.5 8.2
394 6.8 5.3
395 5.4 5.1
396 2.3 4.6
397 7.5 3.9
398 0.9 2.7
399 7.0 4.2
400 6.3 5.5

\$2.19