• Some of the individuals in the sample had taken IL-2 in the recent past when their blood was drawn; others had not. Create a t-test to answer the question as to whether there is a difference in the CD4% between people who have and have not taken IL-2, based on the 4 hour data. Craft a one-sentence conclusion (including the p-value) of the results of the test, the way you might include it in a science paper. Solve the test 2x assuming:
  • Assuming equal variances.
• Assuming unequal variances

• The researcher comes back to you a few weeks later and wants to design two new trials to address the same questions, with higher statistical power. How many subjects to answer the following question: Are there differences between people with/without a history of IL2? Assume that CD4% in both groups will be normally distributed with a standard deviation of 8%. How many people are needed PER GROUP in order to have 80% power to detect a difference of 5% or greater?

	ID	Hours.post.draw	CD4.xCD127	CD8.xCD127	IL2
1	Ad41m	24	66.66667	32.95455	YES
2	Ad41m	4	70	37.93103	YES
3	Ad41m	48	66.66667	34.09091	YES
4	Ad41m	72	62.5	31.03448	YES
5	Ag39i	24	79.41176	37.09677	NO
6	Ag39i	4	79.41176	37.09677	NO
7	Ag39i	48	76.47059	37.31343	NO
8	Ag39i	72	71.875	36.76471	NO
9	AL40T	24	67.64706	23.07692	NO
10	AL40T	4	69.69697	13.84615	NO
11	AL40T	48	67.64706	21.53846	NO
12	AL40T	72	66.66667	24.24242	NO
13	As39l	24	70.37037	28.78788	NO
14	As39l	4	75	28.78788	NO
15	As39l	48	66.66667	27.69231	NO
16	As39l	72	60	24.63768	NO
17	AT59I	24	85.71429	64.91228	NO
18	AT59I	4	90	70.17544	NO
19	AT59I	48	85.71429	68.42105	NO
20	AT59I	72	83.72093	64.28571	NO
21	Ba52m	24	83.33333	41.66667	NO
22	Ba52m	4	79.16667	38.88889	NO
23	Ba52m	48	83.33333	42.46575	NO
24	Ba52m	72	83.33333	39.72603	NO
25	Be45n	24	69.69697	34.92063	YES
26	Be45n	4	71.875	37.5	YES
27	Be45n	48	68.75	37.5	YES
28	Be45n	72	64.51613	35.9375	YES
29	Bl40o	24	77.14286	28.125	YES
30	Bl40o	4	78.78788	28.57143	YES
31	Bl40o	48	75	25.80645	YES
32	Bl40o	72	70.58824	25.39683	YES
33	BL48U	24	66.07143	19.5122	NO
34	BL48U	4	67.27273	20.45455	NO
35	BL48U	48	64.28571	19.04762	NO
36	BL48U	72	63.63636	18.18182	NO
37	Bl51k	24	91.48936	67.92453	YES
38	Bl51k	4	91.30435	73.07692	YES
39	Bl51k	48	91.48936	66.66667	YES
40	Bl51k	72	87.5	64.81481	YES
41	Ch35y	24	81.81818	45.71429	NO
42	Ch35y	4	86.36364	48.57143	NO
43	Ch35y	48	81.81818	42.85714	NO
44	Ch35y	72	73.91304	40	NO
45	Co35t	24	73.68421	60.41667	NO
46	Co35t	4	91.48936	66.66667	NO
47	Co35t	48	89.3617	62.5	NO
48	Co35t	72	84.78261	57.44681	NO
49	DA44I	24	75.75758	23.07692	YES
50	DA44I	4	84.84848	28.125	YES
51	DA44I	48	70.58824	23.80952	YES
52	DA44I	72	67.64706	24.61538	YES
53	DA47N	24	75	38.37209	NO
54	DA47N	4	77.77778	45.88235	NO
55	DA47N	48	75	40	NO
56	DA47N	72	70	38.37209	NO
57	Du50a	24	78.125	34.78261	YES
58	Du50a	4	82.35294	40.57971	YES
59	Du50a	48	77.77778	34.78261	YES
60	Du50a	72	75.75758	30.88235	YES
61	Fo39n	24	83.72093	41.81818	YES
62	Fo39n	4	88.09524	46.2963	YES
63	Fo39n	48	80.95238	42.59259	YES
64	Fo39n	72	72.72727	39.62264	YES
65	GI47S	24	83.33333	33.33333	NO
66	GI47S	4	89.28571	45.07042	NO
67	GI47S	48	85.71429	34.78261	NO
68	GI47S	72	82.75862	35.71429	NO
69	Gi51d	24	40	22.61905	NO
70	Gi51d	4	50	21.68675	NO
71	Gi51d	48	40	20	NO
72	Gi51d	72	25	21.25	NO
73	Go47z	24	90	66.66667	NO
74	Go47z	4	89.65517	63.7931	NO
75	Go47z	48	92.85714	66.66667	NO
76	Go47z	72	89.65517	66.66667	NO
77	Ha38t	24	87.7551	71.73913	NO
78	Ha38t	4	89.79592	76.08696	NO
79	Ha38t	48	87.5	71.73913	NO
80	Ha38t	72	83.67347	65.95745	NO
81	HE49D	24	84.61538	27.53623	NO
82	HE49D	4	88.46154	36.61972	NO
83	HE49D	48	85.18519	29.57746	NO
84	HE49D	72	84.61538	30.55556	NO
85	He53r	24	85.96491	56.41026	YES
86	He53r	4	87.7193	64.10256	YES
87	He53r	48	86.2069	57.5	YES
88	He53r	72	80.70175	52.5	YES
89	Hi68s	24	88	56.16438	YES
90	Hi68s	4	84.61538	56.33803	YES
91	Hi68s	48	84	58.10811	YES
92	Hi68s	72	84	57.74648	YES
93	Ho48g	24	72.72727	38.98305	NO
94	Ho48g	4	75.75758	50.84746	NO
95	Ho48g	48	69.69697	38.98305	NO
96	Ho48g	72	63.63636	31.66667	NO
97	Kn59t	24	80.85106	57.40741	NO
98	Kn59t	4	78.7234	57.69231	NO
99	Kn59t	48	78.7234	57.40741	NO
100	Kn59t	72	79.16667	55.76923	NO
101	La61i	24	82.35294	45.45455	NO
102	La61i	4	84.375	48.48485	NO
103	La61i	48	76.47059	46.9697	NO
104	La61i	72	75.75758	44.77612	NO
105	Lu55s	24	93.22034	60.52632	YES
106	Lu55s	4	93.22034	70.27027	YES
107	Lu55s	48	93.33333	62.16216	YES
108	Lu55s	72	88.33333	56.75676	YES
109	MA48I	24	84.21053	63.15789	NO
110	MA48I	4	88.88889	70.17544	NO
111	MA48I	48	86.11111	67.24138	NO
112	MA48I	72	84.21053	66.10169	NO
113	Mc40u	24	100	32.96703	NO
114	Mc40u	4	100	35.16484	NO
115	Mc40u	48	100	32.6087	NO
116	Mc40u	72	100	32.25806	NO
117	Me42h	24	64	58.33333	NO
118	Me42h	4	64	56.94444	NO
119	Me42h	48	62.5	58.90411	NO
120	Me42h	72	56.52174	56.16438	NO
121	MI52S	24	87.5	25.75758	NO
122	MI52S	4	84.84848	25.75758	NO
123	MI52S	48	84.84848	28.35821	NO
124	MI52S	72	85.29412	30.43478	NO
125	Ou28V	24	66.66667	20	NO
126	Ou28V	4	73.33333	21.25	NO
127	Ou28V	48	66.66667	20	NO
128	Ou28V	72	64.70588	17.72152	NO
129	Ri40h	24	67.64706	41.26984	NO
130	Ri40h	4	66.66667	40.625	NO
131	Ri40h	48	66.66667	41.53846	NO
132	Ri40h	72	63.63636	40	NO
133	RU39K	24	79.41176	53.44828	NO
134	RU39K	4	78.78788	50	NO
135	RU39K	48	79.41176	51.72414	NO
136	RU39K	72	78.78788	54.38596	NO
137	SM43T	24	78.37838	50.87719	NO
138	SM43T	4	78.78788	51.72414	NO
139	SM43T	48	77.77778	53.44828	NO
140	SM43T	72	74.28571	55.9322	NO
141	Sp34h	24	79.31034	36.50794	NO
142	Sp34h	4	81.48148	36.92308	NO
143	Sp34h	48	79.31034	36.92308	NO
144	Sp34h	72	72.41379	33.84615	NO
145	TH56M	24	78.43137	32.43243	YES
146	TH56M	4	82	36.11111	YES
147	TH56M	48	78.84615	34.21053	YES
148	TH56M	72	78.43137	35.89744	YES
149	WH54T	24	90.90909	50	YES
150	WH54T	4	93.58974	54.54545	YES
151	WH54T	48	88.60759	50	YES
152	WH54T	72	87.17949	53.84615	YES
153	WH56T	24	84.78261	38.46154	NO
154	WH56T	4	88.63636	49.01961	NO
155	WH56T	48	84.78261	41.17647	NO
156	WH56T	72	84.78261	42.85714	NO
157	WO54L	24	74.28571	26.98413	YES
158	WO54L	4	85.71429	31.74603	YES
159	WO54L	48	70.27027	30.76923	YES
160	WO54L	72	67.56757	32.30769	YES