Question

1. Generate a hypothesis about the difference between two groups in a dataset.
   • State null hypothesis and alternative hypothesis as an explanation and math equation.
2. Identify the appropriate statistical test of the difference between two groups in a dataset.
   • Provide your statistical rationale.
3. Perform appropriate statistical test of the difference between two groups in a dataset.
4. Interpret statistical results of a data analysis and state whether to accept or reject the null hypothesis based on the p-value and an alpha of .05.
   • Interpret p-value and statistical significance.
5. Summarize practical, administration-related implications of the hypothesis test.

Dataset:                      

clinic1	clinic2
140	169
126	151
30	175
130	115
193	167
137	153
168	115
99	194
135	216
184	149
118	122
109	155
93	185
136	150
102	141
24	135
99	87
104	42
134	96
80	111
30	234
44	158
156	130
150	148
150	105
95	108
51	114
205	113
30	131
92	114
173	61
49	175
137	135
27	198
150	149
182	92
184	127
152	170
147	167
76	175
161	263
143	138
27	161
166	166
139	88
92	152
145	136
176	121
186	174
48	90
92	179
69	171
168	85
27	134
157	123
83	134
139	64
132	153
85	106
97	192
125	115
145	150
129	151
157	166
183	105
50	159
185	160
149	52
157	167
185	103
127	178
110	174
66	80
141	128
125	172
111	154
150	170
162	152
94	95
138	111
162	144
134	136
83	191
157	193
134	144
137	168
76	94
115	126
51	208
150	136
25	201
137	171
148	148
207	214
189	111
104	204
197	189
131	159
151	188
202	174

Answer 1

For the given problem we are assuming that the datasets are independent of one another.

Thus we form the following hypothesis:

H0: There is no significant difference between the means of the two datasets i.e.

H1: There is significant difference between the means of the two datasets i.e.

We need to perform the t-test to analyze the two hypothesis. Thus under the null hypothesis the test statistic is:

where the degrees of freedom are calculated as:

df=(S21n1+S22n2)2/[(1/n1−1)⋅(S21/n1)2+(1/n2−1)⋅(S22/n2)2]

Hence we have:

x1bar = 132.32 and x2bar = 145.03

s21 = 2283.129 and s22 = 1582.514

mu1 - mu2 =0 under the null hypothesis

The value of the test statistic is:

t = 3.491797

df = 191.7 ~ 192

p-value = 0.000595

Since, the p-value is much less than the level of significance i.e. 5%, we reject the null hypothesis at 5% level of significance and conclude that there is significant difference between the means of the two datasets.

With the help of the hypothesis test one confirms using statistics that how two clinics are different from one another with respect to the variable being compared. When the null hypothesis is rejected at a level of significance it confirms the alternative hypothesis. However, in case the null hypothesis is accepted then one does not confirm its acceptance but merely states that it may be a possibility.

Hence, hypothesis testing provides a necessary statistical tool in cases where one needs confirmation regarding the truth about the alternative hypothesis.