Answer this question using R statistical computing environment. Submit your R source file and a report explaining your approach for the question in written form.

2. Refer to the manual dexterity scores of 500 children with learning disabilities and 500 children with no known learning disabilities (given in MANDEXT.csv file). Select a simple random sample of size 10 from population A and an independent simple random sample of size 15 from population B. Do your samples provide sufficient evidence for you to conclude that learning-disabled children, on the average, have lower manual dexterity scores than children without a learning disability? Let ??=0.05. What assumptions are necessary in order for your procedure to be valid?

LDSUBJ	SCORE
1	33
2	20
3	27.5
4	22.5
5	25.8
6	19.8
7	29.9
8	28.4
9	20.8
10	25.6
11	21.4
12	19.1
13	25.3
14	10.7
15	23.5
16	17.7
17	20.6
18	25.2
19	20.9
20	24.6
21	21.2
22	20.5
23	24.3
24	28.8
25	17.7
26	25.2
27	22.4
28	19.7
29	29.4
30	27.3
31	28.9
32	22.4
33	24.7
34	30.4
35	20.9
36	28.8
37	19.5
38	30.3
39	25.3
40	23.3
41	20.1
42	19.1
43	18.5
44	19.5
45	27.3
46	25.8
47	26.7
48	21.7
49	20
50	24.2
51	21.9
52	24.2
53	30.9
54	30.4
55	28
56	27.1
57	22.4
58	28.6
59	27
60	21.1
61	18.4
62	23.1
63	20.9
64	25.6
65	32.6
66	21.9
67	21.5
68	22.6
69	25.2
70	22.2
71	22.7
72	19.7
73	27.6
74	31.6
75	23.5
76	30.6
77	25.9
78	15.9
79	26
80	17.1
81	25.2
82	22.2
83	22.7
84	31.2
85	26.2
86	25.3
87	22.4
88	22.3
89	21.6
90	24.8
91	26.2
92	25.9
93	23.7
94	23.1
95	26.4
96	26
97	29.2
98	20.8
99	17.1
100	21.1
101	30.7
102	31.1
103	22.2
104	14.7
105	24.2
106	23.4
107	27.9
108	34.4
109	29.1
110	23.1
111	24.1
112	25.2
112	23.8
114	20.8
115	23.3
116	29.8
117	35.4
118	23.4
119	21.9
120	27.3
121	25.7
122	24.4
123	25.2
124	24.2
125	8.9
126	23.3
127	24.6
128	29.9
129	27.8
130	31.3
131	23.5
132	28
133	22.9
134	17
15	27.7
136	27.7
137	27.1
138	20.4
139	20.7
140	23.6
141	21.6
142	29.1
142	31
144	19.5
145	21.8
146	27.9
147	24
148	21.5
149	18.4
150	23.6
151	24
152	24
153	26
154	20.7
155	20.4
156	22.7
157	26.8
158	22
159	30.4
160	24.7
161	22.1
162	22.2
163	27.9
164	31.9
165	13.4
166	18.6
167	29.2
168	17.6
169	31.8
170	28.3
171	10.8
172	20.4
173	27.4
174	23.6
175	17.9
176	18.5
177	19.6
178	30.9
179	23.8
180	21.9
181	18.1
182	25.4
183	28.6
184	29.5
185	20.3
186	25.6
187	22.9
188	27.2
189	19
190	18.9
191	24.5
192	22.3
193	222.1
194	18.5
195	21.9
196	28.2
197	37.6
198	16.4
199	23.5
200	25
201	26.1
202	20.1
203	24.2
204	29.4
205	15.4
206	25
207	19.3
208	21.9
209	30.5
210	28.3
211	24.6
212	16.1
213	21.2
214	25.7
215	33
216	28.8
217	26.4
218	263.3
219	27.1
220	18.4
221	20
222	22.7
223	19.6
224	24.1
225	14
226	20.6
227	12.5
228	23.5
229	19.7
230	31.7
231	24.4
232	23.1
233	22
234	26.6
235	33.6
236	14.6
237	26.2
238	24.9
239	24.8
240	30.9
241	25.7
242	31.3
243	23.1
244	17.5
245	22.7
246	23.7
247	24
248	20.7
249	23.8
250	26.9
251	23.6
252	20.9
253	29.7
254	18.1
255	27.9
256	13
257	23.2
258	21.5
259	26.4
260	22.7
261	26.6
262	29.1
263	28.6
264	24.2
265	34.9
266	22.6
267	26.2
268	11.3
269	30
270	22.7
271	22.1
272	18.4
273	18.2
274	18.1
275	26.9
276	27
277	23.8
278	21.9
279	17.4
280	29
281	19
282	30.4
283	26.4
284	26.3
285	28.1
286	27.9
287	19.9
288	24.5
289	22.2
290	24.4
291	29.2
292	23.7
293	24.9
294	17.6
295	24.5
296	31.5
297	15.1
298	23.5
299	25.2
300	26.6
301	21.5
302	31.4
303	27.3
304	24.2
305	27.1
306	27.2
307	27.4
308	19.5
309	21.6
310	21.3
311	26.1
312	30.1
312	27.8
314	31.9
315	22.3
316	24.6
317	25.5
318	25.9
319	21.8
320	21.9
321	26.6
322	30.1
323	26.4
324	16.4
325	29.5
326	20.5
327	21.8
328	22.9
329	14.7
330	25.7
331	24.9
332	23.2
333	20.5
334	24
335	22.9
336	23.6
337	17.5
338	24.9
339	10.1
340	25.3
341	23.8
342	24.8
343	27.3
344	25.1
345	22.9
346	22.2
347	26.2
348	29.3
349	20.7
350	25.1
351	17.4
352	26.7
353	22.2
354	23.1
355	27.5
356	25.5
357	11
358	22.6
359	39.8
360	14.8
361	15.9
362	26.3
363	24.5
364	16.3
365	16.1
366	21.7
367	21.2
368	20.1
369	18.2
370	23.2
371	20.2
372	23.3
373	16.2
374	24.4
375	25.3
376	30.4
377	22.7
378	23.2
379	19.8
380	31.3
381	33.9
382	33.1
383	19.8
384	22.6
385	27.5
386	26.5
387	25.6
388	23.7
389	21.2
390	19.7
391	20.1
392	25.8
393	20.3
394	29.9
395	17.5
396	20.6
397	29.4
398	16
399	21.8
400	23.3
401	30.3
402	33.4
403	27
404	25.8
405	28.9
406	16.5
407	24.5
408	24.7
409	31.4
410	24.6
411	26
412	26.9
412	22.9
414	21.8
415	22.9
416	23.1
417	23.1
418	26.5
419	11.4
420	25.3
421	28.5
422	23.8
4123	28.1
424	29.5
425	27.2
426	23.4
427	15.8
428	23.2
429	25.3
430	30.6
431	23.2
432	30.8
433	22.9
434	27.5
435	20.2
436	26.6
437	28.9
438	23.3
439	21.8
440	18.5
441	29.7
442	30.1
443	24.1
444	19.8
445	18.5
446	26.1
447	13.2
448	23.2
449	37.7
450	30
451	30.9
452	23.3
453	23.7
454	30.9
455	16.2
456	19.9
457	24.8
458	28.3
459	29
460	35
461	23.6
462	28.5
463	33.2
464	29.4
465	25.8
466	25.5
467	17.8
468	23.8
469	31.6
470	25.3
471	24.7
472	21.5
473	26
474	18.2
475	19.8
476	25.6
477	20.1
478	23.7
479	25.2
480	19.8
481	29.3
482	29
483	15.1
484	12.8
485	27.2
486	25.9
487	26.1
488	25
489	28.8
490	22.9
491	28.9
492	17.2
493	19.2
494	21.2
495	28.3
496	31.1
497	25
498	21.9
499	25.2
500	20.8
NORMSUBJ	SCORE
1	32
2	30.6
3	29.1
4	31.8
5	25.3
6	26
7	24.2
8	27.5
9	20.8
10	28.2
11	28.3
12	23.9
13	28.4
14	22.3
15	30.4
16	28.4
17	30
18	30
19	31.2
20	33.5
21	28.5
22	28.1
23	25.7
24	32.8
25	24.5
26	24.5
27	24.9
28	30.6
29	30.4
30	24
31	22.7
32	26.4
33	27
34	25.8
35	28.5
36	26.4
37	29.5
38	26.4
39	28.4
40	25.1
41	26.2
42	28
43	31.4
44	29.5
45	30.1
46	24.7
47	29
48	28
49	25.4
50	25.8
51	23.8
52	27.2
53	27
54	28.8
55	29.9
56	22.4
57	24.1
58	25
59	30.2
60	28.3
61	29.1
62	27
63	30.7
64	32.6
65	23.2
66	29.9
67	25.8
68	20.5
69	30.5
70	28.1
71	20.6
72	29.1
73	22.8
74	21.3
75	24.5
76	29.1
77	22.8
78	23.3
79	22.1
80	32.4
81	31.4
82	25.9
83	32.2
84	30.6
85	25.1
86	30.4
87	29.3
88	28.8
89	25.1
90	26.4
91	28.1
92	32.1
93	26.3
94	26.5
95	26.4
96	32.8
97	26.7
98	31.7
99	27
100	28.3
101	28.5
102	29.4
103	27.2
104	26.3
105	27.6
106	25.7
107	28.1
108	23
109	27.5
110	26.5
111	28.4
112	23.5
113	30.6
114	23.4
115	27.2
116	22.1
117	25.4
118	27.3
119	23.2
120	27.6
121	32.6
122	28
123	27.1
124	27.8
125	26.9
126	25.4
127	26.1
128	23.6
129	29.7
130	26.2
131	30.4
132	27.6
133	26.2
134	26.7
135	28.1
136	30.1
137	23.2
138	24.3
139	23.8
140	23.2
141	24
142	29
143	20
144	29.8
145	23.5
146	22.8
147	25.4
148	27.7
149	26.3
150	27.3
151	28
152	28.5
153	31.8
154	26.6
155	20.4
156	25.7
157	28
158	27.4
159	25
160	32.2
161	29.4
162	30.9
163	24.2
164	23.7
165	27
166	27
167	28
168	29.2
169	29.2
170	27.2
171	24.1
172	27
173	23.8
174	24.4
175	27.6
176	22.7
177	28.9
178	26.7
179	27.5
180	23.5
181	30.3
182	27.7
183	24.9
184	21.8
185	30.7
186	27.2
187	29
188	31.2
189	24.7
190	28.9
191	26.3
192	32
193	25.3
194	28.7
195	27
196	28.5
197	24.9
198	25.1
199	30.4
200	24.9
201	27.3
202	25.8
203	28.6
204	24.8
205	26.9
206	28.9
207	21.6
208	21.6
209	22.3
210	30.5
211	24.6
212	30.1
213	23.3
214	29.7
215	30.2
216	31.8
217	30.7
218	27.2
219	32
220	32.9
221	24.2
222	30.2
223	32.2
224	34.5
225	19.9
226	23
227	32.6
228	31.1
229	26.6
230	31.6
231	22.2
232	30.6
233	26.6
234	29.7
235	28.9
236	30.9
237	27
238	26
239	23.7
240	28.7
241	28.7
242	29.9
243	32.3
244	26.3
245	26.6
246	26.2
247	23.6
248	20.9
249	31.5
250	27.2
251	27.8
252	25.3
253	27.7
254	31.6
255	23.2
256	27.8
257	23.7
258	22.2
259	28.6
260	29.6
261	25.2
262	28.4
263	25.6
264	27.8
265	27.9
266	25.7
267	29.1
268	32
269	26
270	26.8
271	23.5
272	25.5
273	22.5
274	23.6
275	24.1
276	25.1
277	28.3
278	28.2
279	26.8
280	31
281	21.3
282	26.7
283	24.9
284	24.3
285	25.1
286	27.3
287	28.5
288	25.8
289	21.3
290	26.7
291	29.4
292	28.2
293	28.5
294	24.5
295	26.2
296	24.5
297	24.4
298	35.5
299	28
300	29.9
301	27
302	27.1
303	23
304	29.7
305	32.8
306	29.5
307	23.3
308	33.4
309	27.5
310	23.8
311	26.1
312	27
313	28.4
314	27.2
315	26.9
316	26.2
317	29.5
318	28.8
319	24.6
320	26.3
321	23.8
322	28.8
323	22.8
324	31.5
325	25.5
326	27.2
327	28.9
328	24.5
329	28.7
330	33.5
331	30
332	27.8
333	25
334	25.9
335	26.1
336	28.1
337	27.2
338	28.9
339	25.5
340	23
341	33.8
342	23.5
343	23.4
344	25.6
345	27.5
346	30.1
347	27.1
348	33.5
349	26.1
350	26.2
351	29.4
352	26.9
353	24.8
354	28.6
355	30.3
356	22.6
357	25.9
358	26.8
359	32.9
360	27.6
361	25.4
362	22.3
363	25.8
364	27.5
365	29.1
366	31.2
367	31.6
368	18.8
369	29.8
370	25.4
371	25.6
372	30.4
373	28
374	22.7
375	27.1
376	31.6
377	26
378	27.7
379	28
380	31.3
381	26
382	27.5
383	25.2
384	26.2
385	28.8
386	29.8
287	25
388	23.2
389	26
390	30.4
391	28.2
392	27.1
393	34.3
394	29.3
395	25.8
396	27.8
397	28.5
398	27.3
399	26.9
400	31
401	27.6
402	24.2
403	33.2
404	23.6
405	21.3
406	25.3
407	25.9
408	28.1
409	24.8
410	25.6
411	26.3
412	24.7
413	26.1
414	30.8
415	27.4
416	31.9
417	27.5
418	30.2
419	25.6
420	26.9
421	30.3
422	33.1
423	31.6
424	31.7
425	25.9
426	27.7
427	26.8
428	31.5
429	22.1
430	22.2
431	30.3
432	26.1
433	32.7
434	22.9
435	28.2
436	24.9
437	28.3
438	34.3
439	23.6
440	28.9
441	28.9
442	26
443	23.4
444	26.1
445	28.4
446	25.3
447	29.5
448	27.9
449	24.7
450	26.2
451	29.7
452	28.5
453	31.7
454	18.3
455	28
456	24.2
457	30.1
458	24.1
459	27.2
460	26.8
461	25.2
462	31.1
463	24
464	27.8
465	28
466	30.8
467	24.8
468	26.1
469	26
470	30.4
471	25.1
472	27.5
473	23.5
474	28.7
475	27.5
476	22.6
477	21.6
478	23.8
479	28.1
480	30.8
481	28.3
482	27.8
483	25.2
484	22.9
485	26.8
486	29.2
487	27.7
488	28.3
489	20.6
490	29
491	25.4
492	26.5
493	23.3
494	27.9
495	28
496	26.4
497	32.3
498	28.7
499	21.9
500	27.7