A researcher at a marketing firm examines whether the age of a consumer matters when buying athletic clothing. Her initial feeling is that Brand A attracts a younger customer, whereas the more established companies (Brands B and C) draw an older clientele. For 600 recent purchases of athletic clothing, she collects data on a customer's age (Age equals 1 if the customer is under 35, 0 otherwise) and the brand name of the athletic clothing (A, B, or C). A portion of the data is shown in the accompanying table.

Purchase	Age	Brand
1	1	A
2	1	C
600	0	B

Excel Data File BELOW

Purchase	Age	Brand
1	1	A
2	1	C
3	0	A
4	1	B
5	0	C
6	1	A
7	1	A
8	0	B
9	1	B
10	0	C
11	1	A
12	1	A
13	1	A
14	1	C
15	0	A
16	1	A
17	1	C
18	1	B
19	0	B
20	1	A
21	1	B
22	1	A
23	1	B
24	1	C
25	0	C
26	1	A
27	0	B
28	1	B
29	0	A
30	1	B
31	0	B
32	0	B
33	1	C
34	1	A
35	0	A
36	0	B
37	0	B
38	0	B
39	0	C
40	0	C
41	1	A
42	1	A
43	0	A
44	0	A
45	1	C
46	1	A
47	1	A
48	0	C
49	0	A
50	0	C
51	1	A
52	0	A
53	1	C
54	0	C
55	1	B
56	1	C
57	1	B
58	0	B
59	1	B
60	1	B
61	0	B
62	1	C
63	0	A
64	1	B
65	0	B
66	1	B
67	0	C
68	1	A
69	1	A
70	0	A
71	1	A
72	1	A
73	0	A
74	1	A
75	1	A
76	1	A
77	0	A
78	1	A
79	0	A
80	0	A
81	1	A
82	1	A
83	1	A
84	1	A
85	0	A
86	1	A
87	1	A
88	1	A
89	1	A
90	1	A
91	1	A
92	0	A
93	0	A
94	0	A
95	0	A
96	0	A
97	1	A
98	1	A
99	1	A
100	1	A
101	0	A
102	1	A
103	0	A
104	1	A
105	1	A
106	1	A
107	1	A
108	1	A
109	1	A
110	1	A
111	1	C
112	1	C
113	1	C
114	1	B
115	1	A
116	1	C
117	1	B
118	1	A
119	1	A
120	1	A
121	1	B
122	1	C
123	1	A
124	1	B
125	1	C
126	1	B
127	1	C
128	1	A
129	1	A
130	1	B
131	1	A
132	1	C
133	1	C
134	1	A
135	1	A
136	1	B
137	1	A
138	1	C
139	1	B
140	1	A
141	1	C
142	1	C
143	1	A
144	1	A
145	1	C
146	1	B
147	1	B
148	1	A
149	1	C
150	1	A
151	1	C
152	0	A
153	0	B
154	0	C
155	1	B
156	0	B
157	1	A
158	0	B
159	1	A
160	1	C
161	1	A
162	1	C
163	0	A
164	1	B
165	1	A
166	0	B
167	1	A
168	1	A
169	1	A
170	0	A
171	1	B
172	1	B
173	1	A
174	1	C
175	1	A
176	1	A
177	1	B
178	1	B
179	1	A
180	1	A
181	1	B
182	0	B
183	1	A
184	1	B
185	1	C
186	1	B
187	1	B
188	0	A
189	0	A
190	1	C
191	0	C
192	0	C
193	0	C
194	1	B
195	0	A
196	1	A
197	0	B
198	1	B
199	1	A
200	1	A
201	1	A
202	1	B
203	0	A
204	0	C
205	1	A
206	1	B
207	1	A
208	1	C
209	0	B
210	1	C
211	1	A
212	1	B
213	1	A
214	1	C
215	1	C
216	0	B
217	1	A
218	0	B
219	1	A
220	1	C
221	0	C
222	0	C
223	0	C
224	1	A
225	1	B
226	1	B
227	1	A
228	1	B
229	0	A
230	1	A
231	1	A
232	1	B
233	1	B
234	1	B
235	1	B
236	1	A
237	1	A
238	1	B
239	1	C
240	0	C
241	0	B
242	1	B
243	1	C
244	1	C
245	1	B
246	1	A
247	0	C
248	1	A
249	0	C
250	0	B
251	0	C
252	1	A
253	0	B
254	1	B
255	1	A
256	1	A
257	1	C
258	0	B
259	1	C
260	1	B
261	1	B
262	1	C
263	1	A
264	0	A
265	1	A
266	0	B
267	1	B
268	1	A
269	1	C
270	1	A
271	1	A
272	1	A
273	0	A
274	0	B
275	1	A
276	1	B
277	1	C
278	1	A
279	1	C
280	1	C
281	1	B
282	1	B
283	0	C
284	1	A
285	0	C
286	0	C
287	1	B
288	0	C
289	0	B
290	0	C
291	1	B
292	1	B
293	0	C
294	1	A
295	1	B
296	1	A
297	1	A
298	1	A
299	1	A
300	1	B
301	1	A
302	1	C
303	0	C
304	1	C
305	0	C
306	1	C
307	0	B
308	0	C
309	1	C
310	1	A
311	1	C
312	0	B
313	1	B
314	1	A
315	1	A
316	1	A
317	1	C
318	0	B
319	0	C
320	0	B
321	1	B
322	0	C
323	1	B
324	1	A
325	0	A
326	1	B
327	1	B
328	0	C
329	0	C
330	1	A
331	0	A
332	0	B
333	1	A
334	1	B
335	1	A
336	0	B
337	1	B
338	1	C
339	1	C
340	1	A
341	0	B
342	0	A
343	0	B
344	1	B
345	1	B
346	1	A
347	1	C
348	1	A
349	0	C
350	0	A
351	1	B
352	0	A
353	0	C
354	1	A
355	1	A
356	1	C
357	1	C
358	1	C
359	1	A
360	0	C
361	1	C
362	1	B
363	0	A
364	0	B
365	0	C
366	1	A
367	1	A
368	1	C
369	0	B
370	1	A
371	1	B
372	1	B
373	1	C
374	1	A
375	1	C
376	0	C
377	1	B
378	1	A
379	1	C
380	1	B
381	1	C
382	1	A
383	0	B
384	1	A
385	1	A
386	0	A
387	1	A
388	1	A
389	0	B
390	1	C
391	0	B
392	1	A
393	0	C
394	1	A
395	1	B
396	1	A
397	1	A
398	1	B
399	1	C
400	1	C
401	0	A
402	1	A
403	1	B
404	1	C
405	0	C
406	1	B
407	0	A
408	1	B
409	0	C
410	0	A
411	1	C
412	1	A
413	0	B
414	0	C
415	0	A
416	1	A
417	1	B
418	1	A
419	1	A
420	0	C
421	1	A
422	0	B
423	1	A
424	1	B
425	1	A
426	1	A
427	1	B
428	0	C
429	0	A
430	1	A
431	0	B
432	1	B
433	0	A
434	0	A
435	1	A
436	0	A
437	1	B
438	1	C
439	1	A
440	0	B
441	0	B
442	1	B
443	0	C
444	1	A
445	1	A
446	0	A
447	0	B
448	1	B
449	0	B
450	0	B
451	0	C
452	1	A
453	1	A
454	0	B
455	1	A
456	1	C
457	1	C
458	1	B
459	1	B
460	0	C
461	0	C
462	1	C
463	1	B
464	0	B
465	1	B
466	0	C
467	0	C
468	0	B
469	0	B
470	1	B
471	0	B
472	1	B
473	1	B
474	1	A
475	0	A
476	1	C
477	0	B
478	1	B
479	1	A
480	1	B
481	0	B
482	1	B
483	0	A
484	0	A
485	1	C
486	1	A
487	1	C
488	1	A
489	1	C
490	1	B
491	1	B
492	0	A
493	1	A
494	1	A
495	0	C
496	0	C
497	0	C
498	1	A
499	0	C
500	1	A
501	1	C
502	1	B
503	1	A
504	0	A
505	0	C
506	1	B
507	1	B
508	0	B
509	0	B
510	1	B
511	1	C
512	0	B
513	1	A
514	1	A
515	1	A
516	0	C
517	0	A
518	1	C
519	1	A
520	0	A
521	0	B
522	1	A
523	1	A
524	1	C
525	1	B
526	1	C
527	0	B
528	1	B
529	1	A
530	1	B
531	1	A
532	1	B
533	1	B
534	0	C
535	1	A
536	0	A
537	1	C
538	1	C
539	0	C
540	1	B
541	1	A
542	1	C
543	0	A
544	0	C
545	0	B
546	1	A
547	0	B
548	0	C
549	1	C
550	1	B
551	1	B
552	1	A
553	1	A
554	1	B
555	0	C
556	1	A
557	0	C
558	1	A
559	1	C
560	1	B
561	1	A
562	1	B
563	1	A
564	1	A
565	1	A
566	1	B
567	1	A
568	1	C
569	1	A
570	1	B
571	1	C
572	1	B
573	0	B
574	1	B
575	1	A
576	0	C
577	1	A
578	1	A
579	1	A
580	1	B
581	0	C
582	1	C
583	1	C
584	1	B
585	0	C
586	1	B
587	1	A
588	1	B
589	1	A
590	1	B
591	1	B
592	0	A
593	1	C
594	1	B
595	0	A
596	1	A
597	1	C
598	1	B
599	0	C
600	0	B

a-1.Construct a contingency table that cross-classifies the data by Age and Brand. Provide the frequencies in the accompanying table.

a-2.How many of the purchases were for Brand A?

a-3.How many of the purchases were from customers under 35 years old?

b-1.Given that the customer was younger than 35 years old, what is the likelihood that the customer purchased Brand A?(Report the proportion rounded to 2 decimal places.)

b-2.Given that the customer was younger than 35 years old, what is the likelihood that the customer purchased Brand B?(Report the proportion rounded to 2 decimal places.)

b-3.Given that the customer was younger than 35 years old, what is the likelihood that the customer purchased Brand C?(Report the proportion rounded to 2 decimal places.)