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Null Hypothesis

Optional Extra Credit Project Due June 14

Good for up to 10 points, depending on how thorough and creative your work is. Please make sure to show me everything in order to receive the greatest benefit.

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

Attachments

Solution Preview

The solution is in Solution.doc

Optional Extra Credit Project Due June 14

Good for up to 10 points, depending on how thorough and creative your work is. Please make sure to show me everything in order to receive the greatest benefit.

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
...

Solution Summary

The expert evaluates 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:

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