An investment blog suggests that you've been doing this all wrong and should invest in mutual funds only for the short term. So you decide to compare returns at 1 month and 3 months.
a) Using the data provided, check the conditions for this test
b) Test the hypothesis, and find the p-value, if appropriate
c) Find a 95% confidence interval for the mean difference

Name	1 Month(%)	YTD(%)	3 Month(%)	1 Year(%)	3 Year(%)	5 Year(%)
Large Growth	1.12	18.2	3.95	18.83	9.18	13.89
Mid-Cap Growth	0.15	13.69	2.81	14.97	6.83	12.36
Large Blend	0.02	10.58	2.61	14.86	7.52	12.89
Small Growth	-0.43	10.44	3.32	15.97	7.65	12.54
Large Value	-0.89	6	2.06	12.47	6.11	12.08
Mid-Cap Blend	-1.15	5.96	1.45	11.81	5.24	12.46
Mid-Cap Value	-1.59	3.75	1.2	11.11	5.13	12.42
Small Blend	-1.71	2.21	1.56	12.68	5.82	12.09
Small Value	-2.44	-1.7	1.03	11.19	4.56	11.49
Target-Date 2060+	0.35	13.21	3.31	15.32	6.43	11.03
Target-Date 2055	0.33	13.07	3.29	15.06	6.02	10.34
Target-Date 2050	0.37	12.83	3.23	14.75	5.89	9.97
Target-Date 2045	0.34	12.77	3.22	14.69	5.82	9.97
Target-Date 2040	0.39	12.25	3.08	13.98	5.66	9.59
Target-Date 2035	0.4	11.7	2.97	13.18	5.45	9.31
Target-Date 2030	0.47	10.66	2.73	11.61	5.08	8.44
World Allocation	0.38	9.85	2.63	9.87	2.55	5.81
Target-Date 2025	0.49	9.61	2.5	10.12	4.65	7.75
Convertibles	-0.04	8.46	2.45	10.44	3.21	8.43
Target-Date 2020	0.53	8.37	2.21	8.47	4.16	6.62
Target-Date 2015	0.51	7.78	2.04	7.73	4.02	6.43
Tactical Allocation	0.37	7.35	2.07	8.01	1.86	4.72
Target Date 2010	0.54	7.17	1.93	6.99	3.86	5.71
Target-Date Retirement	0.54	6.21	1.72	5.72	3.15	4.37
Allocation--15% to 30% Equity	0.38	4.61	1.35	4.41	2.26	3.42
India Equity	-0.59	32.99	5.73	21.06	9.34	13.34
China Region	3.54	31.59	12.69	25.64	8.09	10.94
Latin America Stock	5.92	27.91	14.81	25.11	-5.17	-2.5
Pacific/Asia ex-Japan Stk	1.37	27.3	7.39	20.11	5.09	8.36
Diversified Emerging Mkts	2.19	26.29	8.39	21.66	1.72	5.18
Foreign Small/Mid Growth	1.27	25.14	5.3	20.07	6.8	11.53
Foreign Large Growth	0.95	22.86	4.3	17.92	4.82	9.06
Foreign Small/Mid Blend	0.77	21.94	4.69	21.97	6.03	11.19
Diversified Pacific/Asia	0.96	19.83	5.6	17.98	5.78	9.96
Foreign Small/Mid Value	0.77	19.4	5.03	20.09	3.91	10.2
Foreign Large Blend	0.24	17.9	3.27	17.2	2.97	7.93
Europe Stock	0.02	17.63	1.06	18.88	3.62	9.27
Foreign Large Value	-0.05	15.51	3.03	17.45	1.28	7.26
World Large Stock	0.23	15.37	3.12	16.04	5.42	10.53
Japan Stock	0.32	12.41	3.75	19.46	9.06	13.25
Emerging-Markets Local-Currency Bond	1.6	13.1	4.1	8.47	-1.22	-0.37
Emerging Markets Bond	1.46	8.99	2.49	6.83	3.63	3.73
Preferred Stock	-0.04	8.73	2.43	5.85	5.24	5.7
Long Government	3.27	8.4	3.26	-5.72	4.68	2.54
Long-Term Bond	1.58	8.17	2.81	0.87	4.73	4.52
World Bond	0.7	6.42	2.18	2.57	0.96	1.57
High Yield Bond	-0.04	5.21	1.1	7.66	3.22	5.3
Multisector Bond	0.46	5.12	1.46	4.85	3.01	3.76
Corporate Bond	0.63	5.05	1.66	2.27	3.35	3.62
Intermediate-Term Bond	0.75	3.77	1.21	1.27	2.39	2.3
Nontraditional Bond	0.03	3	0.8	4.28	1.87	2.27
Intermediate Government	0.69	2.21	0.66	-0.3	1.65	1.12
Bank Loan	-0.17	2.11	0.45	4.84	2.76	3.59
Inflation-Protected Bond	0.84	2.07	0.49	0.76	0.45	-0.12
Short-Term Bond	0.22	1.79	0.55	1.54	1.33	1.29
Ultrashort Bond	0.12	1.03	0.37	1.38	0.85	0.82
Short Government	0.24	0.94	0.31	0.28	0.66	0.42
High Yield Muni	1.03	6.37	1.57	0.85	4.67	4.23
Muni California Long	0.81	5.27	1.26	0.1	3.81	3.85
Muni National Long	0.84	4.99	1.34	0.16	3.41	3.12
Muni California Intermediate	0.76	4.7	1.11	0.2	2.63	2.71
Muni National Interm	0.73	4.54	1.08	0.5	2.64	2.55
Muni New York Long	0.6	4.54	0.95	0.2	3.35	2.84
Muni New Jersey	0.98	4.45	1.33	0.07	2.89	2.52
Muni Pennsylvania	0.66	4.28	0.96	0.34	3.1	2.68
Muni Massachusetts	0.63	4.09	0.86	-0.11	2.69	2.3
Muni New York Intermediate	0.55	4.07	0.85	0.12	2.57	2.39
Muni Minnesota	0.66	3.99	0.93	0.26	2.66	2.52
Muni Ohio	0.56	3.75	0.72	0	2.64	2.38
Muni Single State Interm	0.59	3.67	0.79	0.04	2.36	2.16
Muni Single State Long	0.56	3.43	0.73	-0.23	2.67	2.23
Muni Single State Short	0.42	2.61	0.56	0.34	1.24	1.16
Muni National Short	0.34	2.16	0.51	0.68	0.93	0.95
Long-Short Equity	0.02	6.04	1.72	7.87	2.6	5.67
Option Writing	0.29	5.49	1.68	7.07	2.92	5.18
Multialternative	0.33	3.17	1.06	3.54	0.81	2.7
Long-Short Credit	-0.01	2.2	0.59	3.13	0.86	1.97
Multicurrency	-0.37	1.88	0.12	1.89	0.05	-0.53
Market Neutral	0.19	0.85	0.68	2.64	-0.1	0.55
Managed Futures	0.91	-1.14	-0.68	-4.92	1.35	0.91
Bear Market	-0.62	-17.83	-6.09	-24.38	-17.17	-22.3
Commodities Precious Metals	4.02	12.15	2.91	0.05	-1.56	-6.45
Commodities Broad Basket	0.64	-2.4	2.46	2.75	-12.46	-10.04
Technology	1.98	25.2	4.48	28.34	14.44	17.62
Health	2.37	22.01	9.29	16.61	8.49	17.47
Infrastructure	1.41	16.78	3.54	13.53	3.75	10.04
Equity Precious Metals	6.05	15.19	9.42	-3.06	-1.85	-9.68
Utilities	2.41	13.61	3.22	15.3	8.83	11.61
Global Real Estate	0.34	10.26	3.42	3.25	3.64	7.21
Industrials	0.75	9.62	2.84	19.41	8.96	16.01
Consumer Cyclical	-1.96	7.88	-0.96	10.21	6.33	12.58
Communications	0.03	7.54	1.76	10.49	6.81	10.14
Consumer Defensive	-0.97	7.13	-1.1	4.42	8.35	12.02
Financial	-2.22	4.92	4.42	21.6	8.97	14.61
Real Estate	-0.13	4.38	3	0.35	6.81	8.51
Natural Resources	-0.35	4.05	4.28	11.74	-4.7	1.27
Energy Limited Partnership	-4.09	-6.85	-2.38	-0.5	-12.17	-0.45
Equity Energy	-6.22	-20.1	-5.76	-9.79	-19.39	-6.29