Graphical methods to present the two populations

Question

1) Test of two means. You should select a hypothesis you are interested in testing and then use a test of two means to test this hypothesis. For example, you may be interested in testing whether the GPA of females is higher than that of males in that class. One is going to draw the inference by using a random sample with replacement of size 25 from each group. Report the p-value of the test. Perform the test using a significance level a = .05. Use graphical methods to present the two populations of interest.

Data

Sex	Height	Weight	GPA	LArm	RArm	LFoot	RFoot	Smoker
0	67	125	2.4	25.5	25.5	27.2	27	N
1	68	140	2.81	23	23	23	23	N
1	67	142	2.8	26	27	22	22	N
1	60	110	3.6	24	24	24	24.5	S
1	64	97	2.5	24	24	21	21	S
1	61	106	3.85	21.5	21.5	22	22	N
0	79	210	3.33	30.5	30.5	28	28	N
1	61	110	1.94	23.5	22.5	21.5	21	N
0	71	150	3.46	26	26	29	28	N
1	66	145	2.56	24	25	24	25	N
1	59.5	113	3.33	21	23	20	22	S
0	71	175	2.8	27	27	27.5	26	N
0	72	145	2.85	25.5	25	28	28	N
1	55	110	*	24	23	22	23.5	S
1	64	112	3.59	23	23.5	23	23.5	S
1	65	135	3.33	22	23	21	20	S
1	65	135	3.25	23	23	26	27	N
1	71	140	3.63	27	27	25	25	N
1	68	130	3.7	25	25	24	25	N
0	71	152	2.8	25.4	27.9	27.9	27.9	N
1	67	127	3.13	25.5	25.5	24.5	24.5	N
0	70	143	3.53	26.5	27	26.3	26.3	N
1	68	165	2.13	24.5	24.5	24.5	25.5	S
0	72	160	2.5	25	26	28.5	29	S
0	71	185	3	28	27	29	27	N
1	65	114	2.5	25.4	25	24.7	24.5	N
1	67	116	3.33	23	24.5	22.5	23	N
1	66	113	3.3	25.5	26	25.3	25.5	N
1	63	145	2.4	21	22	24	25	S
1	62	116	3.3	25	25	27	25	S
0	70.5	155	2.53	25.5	28	26	25.5	S
1	64	107	3.24	24.5	24	23.5	24.5	S
1	64	104	3.4	24.5	24.1	22.5	22.8	N
1	69	137	2.6	23.5	23.5	24	24.5	N
0	75	200	3.1	31	28	28	29	S
0	65	150	2.89	25	25	23.5	23	N
1	67	140	3.1	25.5	25	25	25.5	N
1	65	125	*	23.5	23	24	23.5	N
0	75	240	2.7	27	27.5	31	32	S
1	57	140	3.16	22	24	25.5	24.3	S
0	68	135	3	23.5	25.5	25	25	S
0	73	178	2.3	26	25	29	29.5	N
1	68	122	1.89	24.5	24.6	24.3	24.5	N
1	62	145	2	23.4	23.5	23.8	24	N
0	68	190	2.9	25	25	25	25.5	N
0	73.5	180	3.33	26.2	26.5	26.2	26.5	N
1	63	125	2	27.5	27.5	22.5	22.5	N
0	72.5	165	2.5	24.8	24.5	28	27.5	N
1	66	115	2	27	27.5	22.5	23.5	N
1	68	125	3.91	25.5	25	25.5	25	S
0	72	210	2.8	26.5	26.5	28.5	28.5	N
1	63	118	3.63	23	23	24	23	N
1	65	135	3	22.5	23	22.9	23.2	N
0	75	225	1.24	24.5	24.5	30	30	N
1	69	145	3.31	25.5	26.5	25.5	25.5	N
1	72	240	3.78	28	28	26.2	25.7	N
1	69	170	3.1	27	26.5	28	28.5	N
1	62	105	2.8	23	22	24	23	N
1	64	125	3.4	24	23.5	23.5	23.5	N
1	62.5	130	3.1	22.5	22	23.5	24.5	N
0	78	190	3	30	29.5	31.5	32	N
1	63	115	2.8	22	22.5	21	22	N
0	73	280	2.1	26.5	26.5	26	26	S
1	69	125	3.72	24.5	24.5	24.5	24.5	N
1	62.5	120	2.17	24	24	23	23.5	N
1	63	145	2.65	22.5	21	22.8	22.5	S
1	63	132	3.48	22.5	22	24.5	23	S
0	69.5	195	3.1	27	27	27	27	N
0	69	168	2.5	25	25	23	23	N
1	70	*	1.5	29	29	29	29	N
1	60.5	105	2.17	20.5	21	23	22.5	S
1	65	112	3.31	21.5	22	22	23.5	S
0	72	215	2.84	26.5	26.5	27.5	27.2	N
1	69	150	2.98	29	29	28.5	28.7	N
1	70	150	2.56	26.7	25.4	26.7	25.4	N
1	67	125	3.23	23	25	25	23	S
1	64	135	3.67	23.5	24	22	22.6	N
0	70	185	2.3	25	26	25.5	26	S
1	71	127	2.8	25.5	28	25.5	28	S
0	72	178	2.7	25.5	28	29.5	29.7	S
1	66	123	2.49	25.5	25.5	24	25.5	N
0	65.5	145	3.55	26	25	27	27	S
1	71	135	3	25.5	28	25.5	28	N
0	68	135	2.4	27	27	27	27	S
0	66.5	145	3.61	27	27	27	27	N
1	67	145	3.2	26.1	27.7	24.9	25.4	N
0	69	193	2.95	28	28	27.2	27.8	N
1	66	125	3.23	24	24.5	24	24.5	S
0	71	148	2.5	28	28.5	28	27	N
1	65	125	2.8	25	25	22	23	S
1	62	120	3.55	26	26	23	23	N
1	65	119	2.9	24	26	23	23	S
1	68	160	3.35	26.5	26.5	23.5	22.5	N
1	67	140	3.74	23.3	24	24.5	23.5	S
1	62.5	115	2.5	24	24	24	24	N
1	64	125	3.76	23.4	23.4	23.4	23.5	N
1	61	95	3.15	22.2	22.2	22	22.2	N
1	62	126	3.33	24.6	23.9	23.5	23.8	S
1	62.5	165	2.5	24.9	25.5	23.9	23.7	N
0	70	167	2.6	27	27	26	26	S
0	73	250	2.9	26	26	29	29.5	N
0	73.5	280	3.54	26	28.5	29	30	S
0	79	180	2.6	30.5	30.5	32	32	N
0	71	175	3.48	29	28	28	30.5	S
1	63	120	3	27	27	27	27	S
0	72.5	125	3	27	27	28	28	N
0	69.5	156	3.45	26	26	24	24	S
0	75	185	2.9	30	30	30	30	N
1	62	130	2.33	23.5	23.5	23.5	23	N
0	67	140	1.96	26	26.5	26.5	27	N
1	64.5	120	3.62	22.5	21.5	23.3	23	N
1	66	140	2.9	25.5	25.5	23	23	S
0	69	155	2.5	25	25.5	25.5	25.5	N
1	60	105	2.82	21.5	20.5	19.5	20.5	N
1	67	125	3	25.5	25.5	22	23	N
1	65	115	3.7	25.5	26.5	23	21	N
1	66	130	3.37	24.5	25	22.5	22.5	N
0	69	170	3.5	28	26	25	26	N
0	73	247	2.57	27.2	25.9	27.2	25.9	N
0	73.5	172	3.43	25.5	25.5	26.5	26.5	N
0	65	147	3.69	24	25	24	25.5	N
1	67	*	3.48	23	23	23	23	N
1	67.5	*	3.1	24	26	26	24	N
1	62	140	2.58	22.5	22.5	23	23	S
1	64	120	3.35	23.5	23.5	22	22	S
1	63	110	3.66	26	26	24	24	S
1	65	115	3.81	25.5	25.5	23.5	23.5	N
1	61	115	3.5	25	24	23.5	24	N
0	73	165	2.2	30	29	23.5	24	N
0	74	180	3.6	29	31	28	28	N
0	72	182	2.89	27	27	27.5	28.5	N
1	65	130	3.89	25.5	26	23	22.5	N
0	73	160	3.78	23	23	28.5	27.5	N
0	74	190	2.3	28	27	29	30	N
0	75	180	2.67	29.5	29.5	29	29	N
1	70	165	3	29	29	26.5	26.5	N
1	62	140	2.8	22	22	24	24	N
0	68	165	3.53	26	28	27.5	27.5	S
1	57	125	2.6	23	23	23	23	S
0	72	160	3.2	28.5	28	26.5	27.5	N
1	66	128	3.54	24.5	25.5	24.5	24	N
1	65	115	3.32	24	24	24	23.5	N
1	63	135	3.27	24.5	25.5	25	25	N
1	66	118	2.9	23.5	22.9	22.9	24.1	N
1	74	130	2.5	22.9	22.9	21.6	20.3	N
1	64	130	3.17	25.4	25.4	24.1	22.9	S
1	67	140	2.79	25.4	26.7	25.4	24.1	S
0	71	174	3.67	25.4	26.7	26.7	26.7	N
1	60	118	3.34	23	23	20.5	21.5	N
1	64.5	133	3.13	24.5	24.5	25	25.5	N
1	61.5	107	3.49	23	23	23	24	N
1	64	145	2.58	24	25	23	23	S
0	66	150	2.89	24	25	25.5	26	N
1	70.5	165	*	28	28	28	28	N
1	69	143	2.9	25	25	25	24.5	N
1	70	155	3.14	25.5	26.5	27	26.5	S
1	64	138	3.69	23.5	23.5	24	23.5	N
1	62	147	2.9	23.5	23.5	21.5	23	N
0	77	245	2.91	24	26	29	29.5	S
1	62	130	3.2	22.5	23	21.5	21	N
1	69	135	2.47	24.5	24.5	25.5	26	S
0	70	150	2.98	29	29	27	28	N
0	71	135	1.9	25.5	26	25.8	26.8	N
0	71.5	160	3.2	28.6	28.1	27.4	28.5	S
1	67.5	110	3.9	28	28.5	24.5	25	N
0	69	155	2.7	25.5	25.5	27	26.5	S
1	63	96	2.93	23	23	22	22	N
1	65	140	3.4	25	24	23	25.5	S
1	66.5	120	3.33	24	24	24	22	N
1	67	130	3.3	26.5	26.5	23	22	S
0	73	155	3	26.5	27	27	26.5	N
1	63	105	3.56	25	26.5	24	23	N
0	73	160	2.55	26.5	27	27	27.5	N
1	63	112	3	23	24	23	22	S
1	68	125	3.39	25	25	25	24.5	N
1	69	132	3.1	25.5	25.5	25	25	N
1	69	175	3	23.5	26	27	25.5	N
1	63	150	2.9	24	24	23.5	24	N
1	64	105	3.62	21	23	22.3	22	N
1	69	135	*	28	25.5	26.5	26	N
1	63	134	2.8	24	23.5	24	23.5	S
1	64	115	2.75	24	23	23	22	N
1	63	123	2.4	24	24	24	23.5	N
1	67	170	3.28	28	27.5	24.5	24.5	N
0	71	162	3.9	23.5	23	27	27.5	N
1	68	140	3.65	24.5	22.8	24.7	24.5	S
1	64	115	2.67	24	24.5	24.7	24.3	N
0	73	205	3.1	29	29	27.5	27.5	N
1	67.5	130	3	24	23.5	26	24.5	S
1	67	145	1.83	24.6	24.3	26	26.3	N
1	60.5	125	2.7	24.1	24.1	24.4	23.9	S
0	69	180	3.86	25.5	25.5	29	29	N
1	65.5	135	3.52	24.5	25	24	24	S
1	64	140	2.1	25	24.5	22.5	22.5	N
0	76	185	3	28	27	30	30	S
1	64	135	3.4	25	24.5	23	22.5	N
1	63	127	3.3	22	22	24	25	N
1	62	115	2.17	23.5	24	22.7	23	N
1	62	135	*	25	25	22.8	23	N
1	70.5	142	3.58	24.5	25	26	26.5	N
1	67	140	3.44	24	24.5	25	24.5	S
1	68	135	2.2	24	24	25.5	25.5	S
0	71	178	3.2	29.5	28.5	29	28.5	N
1	67	135	*	25	25	25.5	25	N
1	64	127	2.2	26.5	26.5	26.5	26.5	N
1	70	153	3.17	22	22	23.5	23.5	N
1	62	110	3.44	21.5	21.5	23.5	22.5	S
0	73	165	3.62	28	28.4	30.6	31.4	N
0	79	165	2.45	28	25	29	27.5	N
0	75	160	3.8	27.5	27.5	29	27.6	N
0	71	170	3.2	28	27	31	31.3	S
1	65	117	2.7	24.1	24.1	24.1	24.1	N
0	69.5	185	3.2	26.5	27	27	27	N