In: Statistics and Probability
You have heard from idle chatter that most students don't declare a major in their MBA programs. You took a sample of 200 students (in the data file). Conduct a one-sample hypothesis test to determine if the proportion without a major is greater than 50%. Use a .05 significance level.
ID | Gender | Major | Employ | Age | MBA_GPA |
1 | 0 | No Major | Unemployed | 39 | 2.82 |
2 | 1 | No Major | Full Time | 55 | 4 |
3 | 0 | No Major | Part Time | 43 | 3.45 |
4 | 0 | No Major | Full Time | 56 | 2.61 |
5 | 1 | No Major | Full Time | 38 | 3.5 |
6 | 0 | No Major | Unemployed | 54 | 4 |
7 | 0 | No Major | Full Time | 30 | 3 |
8 | 0 | No Major | Full Time | 37 | 2.5 |
9 | 0 | No Major | Part Time | 38 | 2.84 |
10 | 0 | No Major | Full Time | 42 | 3.72 |
11 | 0 | No Major | Part Time | 52 | 3.21 |
12 | 0 | No Major | Full Time | 35 | 3.44 |
13 | 0 | No Major | Full Time | 37 | 3.65 |
14 | 0 | No Major | Full Time | 53 | 3.02 |
15 | 0 | No Major | Part Time | 51 | 3.03 |
16 | 1 | No Major | Full Time | 40 | 3.8 |
17 | 0 | Finance | Full Time | 33 | 4 |
18 | 0 | No Major | Part Time | 53 | 3.26 |
19 | 0 | No Major | Full Time | 43 | 3.53 |
20 | 0 | Finance | Unemployed | 35 | 3.75 |
21 | 0 | No Major | Full Time | 57 | 3.15 |
22 | 1 | No Major | Part Time | 32 | 3.66 |
23 | 1 | No Major | Full Time | 59 | 3.36 |
24 | 1 | No Major | Full Time | 48 | 3.79 |
25 | 1 | No Major | Part Time | 34 | 2.85 |
26 | 1 | No Major | Full Time | 53 | 3.74 |
27 | 1 | No Major | Part Time | 35 | 3.23 |
28 | 1 | No Major | Unemployed | 38 | 3.52 |
29 | 1 | No Major | Part Time | 37 | 3.32 |
30 | 0 | Finance | Full Time | 46 | 2.89 |
31 | 0 | No Major | Full Time | 44 | 2.83 |
32 | 0 | No Major | Unemployed | 31 | 2.93 |
33 | 0 | No Major | Full Time | 51 | 3.71 |
34 | 0 | Finance | Full Time | 47 | 3.47 |
35 | 0 | No Major | Part Time | 56 | 3.52 |
36 | 1 | Finance | Part Time | 42 | 2.83 |
37 | 0 | Finance | Full Time | 44 | 3.64 |
38 | 0 | No Major | Unemployed | 54 | 2.96 |
39 | 0 | Finance | Full Time | 51 | 3.59 |
40 | 0 | No Major | Part Time | 42 | 3.33 |
41 | 0 | Finance | Full Time | 45 | 3.38 |
42 | 0 | Finance | Full Time | 55 | 3.44 |
43 | 0 | No Major | Full Time | 47 | 3.31 |
44 | 1 | Finance | Unemployed | 43 | 3.03 |
45 | 0 | Finance | Full Time | 57 | 3.26 |
46 | 1 | Finance | Full Time | 36 | 3.04 |
47 | 1 | No Major | Part Time | 58 | 2.98 |
48 | 1 | Finance | Full Time | 46 | 2.8 |
49 | 1 | Finance | Full Time | 53 | 3.75 |
50 | 0 | Finance | Full Time | 59 | 3.64 |
51 | 0 | No Major | Full Time | 49 | 3.65 |
52 | 0 | Finance | Full Time | 34 | 3.18 |
53 | 0 | No Major | Full Time | 46 | 3.44 |
54 | 1 | Finance | Unemployed | 46 | 3.06 |
55 | 1 | Finance | Full Time | 33 | 3.51 |
56 | 1 | Marketing | Part Time | 56 | 3.33 |
57 | 1 | Marketing | Full Time | 39 | 2.81 |
58 | 1 | Marketing | Full Time | 51 | 3.64 |
59 | 1 | Leadership | Part Time | 55 | 3.05 |
60 | 1 | Leadership | Full Time | 38 | 2.85 |
61 | 1 | Marketing | Full Time | 33 | 3.56 |
62 | 1 | Marketing | Full Time | 34 | 2.92 |
63 | 1 | Marketing | Full Time | 31 | 3.35 |
64 | 1 | Marketing | Full Time | 37 | 3.46 |
65 | 1 | Marketing | Full Time | 46 | 3.59 |
66 | 1 | No Major | Unemployed | 31 | 3.11 |
67 | 1 | No Major | Full Time | 47 | 3.65 |
68 | 1 | No Major | Part Time | 54 | 3.17 |
69 | 1 | No Major | Full Time | 52 | 2.97 |
70 | 1 | Marketing | Part Time | 43 | 3.77 |
71 | 1 | Leadership | Full Time | 44 | 3.21 |
72 | 1 | Leadership | Part Time | 34 | 3.17 |
73 | 1 | Leadership | Full Time | 59 | 3.65 |
74 | 1 | Leadership | Full Time | 45 | 2.94 |
75 | 1 | Leadership | Full Time | 30 | 3.53 |
76 | 1 | No Major | Full Time | 32 | 3.65 |
77 | 1 | Leadership | Full Time | 32 | 3.61 |
78 | 1 | No Major | Full Time | 40 | 3.7 |
79 | 1 | Leadership | Full Time | 48 | 2.91 |
80 | 1 | Leadership | Unemployed | 51 | 3.09 |
81 | 1 | Leadership | Full Time | 30 | 3.77 |
82 | 1 | Leadership | Full Time | 31 | 3.79 |
83 | 1 | Leadership | Full Time | 35 | 3.59 |
84 | 1 | Leadership | Full Time | 33 | 3.38 |
85 | 1 | No Major | Full Time | 35 | 4 |
86 | 1 | Marketing | Full Time | 31 | 2.97 |
87 | 1 | Marketing | Full Time | 38 | 3.44 |
88 | 1 | No Major | Part Time | 46 | 3.64 |
89 | 1 | Finance | Full Time | 45 | 3.48 |
90 | 1 | Finance | Full Time | 59 | 2.76 |
91 | 1 | Finance | Full Time | 58 | 3.73 |
92 | 1 | Finance | Full Time | 46 | 2.91 |
93 | 1 | Finance | Full Time | 35 | 3.78 |
94 | 1 | Finance | Part Time | 53 | 3.5 |
95 | 1 | Finance | Full Time | 31 | 3.13 |
96 | 1 | Finance | Full Time | 50 | 3.14 |
97 | 1 | Finance | Full Time | 38 | 3.24 |
98 | 1 | Finance | Full Time | 50 | 3.56 |
99 | 1 | Finance | Full Time | 48 | 3.16 |
100 | 1 | Finance | Full Time | 53 | 3.53 |
101 | 0 | No Major | Unemployed | 53 | 3.7 |
102 | 0 | Marketing | Full Time | 30 | 3.3 |
103 | 0 | Marketing | Part Time | 32 | 4 |
104 | 0 | Leadership | Full Time | 42 | 3.5 |
105 | 0 | Leadership | Full Time | 56 | 3.39 |
106 | 0 | No Major | Full Time | 46 | 3.65 |
107 | 0 | Leadership | Full Time | 49 | 2.78 |
108 | 0 | No Major | Part Time | 32 | 3.44 |
109 | 0 | No Major | Full Time | 36 | 3.88 |
110 | 0 | No Major | Full Time | 42 | 2.84 |
111 | 0 | No Major | Part Time | 37 | 3.53 |
112 | 0 | No Major | Full Time | 31 | 3.22 |
113 | 0 | No Major | Full Time | 31 | 3.56 |
114 | 0 | No Major | Unemployed | 42 | 3.2 |
115 | 0 | No Major | Full Time | 39 | 3.56 |
116 | 0 | No Major | Full Time | 47 | 3.41 |
117 | 0 | Leadership | Part Time | 28 | 3.56 |
118 | 0 | Leadership | Unemployed | 28 | 3.34 |
119 | 0 | Leadership | Full Time | 52 | 2.56 |
120 | 0 | Leadership | Part Time | 35 | 3.76 |
121 | 1 | Finance | Full Time | 38 | 3.55 |
122 | 1 | No Major | Full Time | 44 | 3.88 |
123 | 1 | No Major | Part Time | 38 | 3.31 |
124 | 1 | Finance | Full Time | 52 | 3.09 |
125 | 1 | Finance | Unemployed | 53 | 3.82 |
126 | 1 | Finance | Part Time | 53 | 3.01 |
127 | 1 | Finance | Full Time | 31 | 3.66 |
128 | 1 | Finance | Part Time | 47 | 3.64 |
129 | 1 | Finance | Full Time | 51 | 3.59 |
130 | 1 | Finance | Unemployed | 37 | 3.49 |
131 | 1 | Finance | Part Time | 46 | 3.13 |
132 | 1 | Finance | Full Time | 48 | 3.83 |
133 | 1 | Leadership | Full Time | 54 | 3.04 |
134 | 1 | Leadership | Full Time | 48 | 3.91 |
135 | 1 | Leadership | Full Time | 36 | 3.56 |
136 | 1 | Finance | Unemployed | 39 | 3.96 |
137 | 1 | Finance | Full Time | 28 | 3.46 |
138 | 1 | Finance | Part Time | 45 | 3.22 |
139 | 1 | Finance | Full Time | 31 | 3.27 |
140 | 1 | Finance | Full Time | 47 | 3.43 |
141 | 1 | Finance | Part Time | 35 | 3.85 |
142 | 1 | Finance | Full Time | 52 | 3.89 |
143 | 0 | Finance | Part Time | 52 | 3.37 |
144 | 1 | Finance | Unemployed | 55 | 3.32 |
145 | 1 | Finance | Full Time | 52 | 3.54 |
146 | 1 | Finance | Part Time | 46 | 3.8 |
147 | 1 | Leadership | Full Time | 31 | 3.74 |
148 | 1 | Leadership | Unemployed | 33 | 3.6 |
149 | 1 | Leadership | Part Time | 45 | 2.6 |
150 | 1 | Leadership | Unemployed | 50 | 3.8 |
151 | 1 | No Major | Part Time | 33 | 2.67 |
152 | 1 | No Major | Full Time | 37 | 3.95 |
153 | 1 | No Major | Unemployed | 33 | 3.56 |
154 | 1 | Marketing | Full Time | 46 | 3.79 |
155 | 1 | Marketing | Unemployed | 55 | 3.93 |
156 | 1 | Marketing | Full Time | 30 | 3.79 |
157 | 1 | Marketing | Full Time | 51 | 3.71 |
158 | 1 | Marketing | Unemployed | 35 | 3.05 |
159 | 1 | Marketing | Unemployed | 40 | 3.22 |
160 | 0 | Marketing | Part Time | 29 | 3.85 |
161 | 1 | Marketing | Full Time | 52 | 3.82 |
162 | 1 | Marketing | Unemployed | 27 | 3.23 |
163 | 1 | Marketing | Full Time | 51 | 3.56 |
164 | 0 | Marketing | Part Time | 56 | 3.53 |
165 | 1 | Marketing | Unemployed | 35 | 3.62 |
166 | 1 | Leadership | Full Time | 46 | 3.8 |
167 | 1 | Leadership | Part Time | 39 | 3.47 |
168 | 1 | Leadership | Full Time | 31 | 3.64 |
169 | 1 | Leadership | Part Time | 52 | 3.03 |
170 | 1 | Leadership | Unemployed | 35 | 3.17 |
171 | 1 | Leadership | Full Time | 32 | 3.22 |
172 | 0 | Leadership | Part Time | 44 | 3.92 |
173 | 1 | Leadership | Unemployed | 43 | 3.82 |
174 | 1 | Leadership | Part Time | 38 | 3.26 |
175 | 1 | Leadership | Full Time | 54 | 3.8 |
176 | 1 | Leadership | Full Time | 30 | 3.2 |
177 | 0 | Leadership | Part Time | 38 | 3.46 |
178 | 1 | Leadership | Full Time | 45 | 3.67 |
179 | 1 | Leadership | Unemployed | 48 | 4 |
180 | 1 | Leadership | Full Time | 43 | 3.66 |
181 | 0 | Leadership | Full Time | 34 | 3.96 |
182 | 1 | Leadership | Full Time | 54 | 3.75 |
183 | 1 | Leadership | Full Time | 36 | 3.83 |
184 | 1 | Leadership | Full Time | 45 | 3.55 |
185 | 0 | Leadership | Unemployed | 55 | 3.36 |
186 | 1 | Leadership | Part Time | 45 | 3.21 |
187 | 1 | Leadership | Part Time | 34 | 2.97 |
188 | 0 | Leadership | Part Time | 54 | 3.99 |
189 | 1 | Leadership | Full Time | 36 | 3.07 |
190 | 1 | Leadership | Full Time | 24 | 3.65 |
191 | 1 | Leadership | Full Time | 34 | 3.67 |
192 | 1 | Leadership | Full Time | 45 | 3.06 |
193 | 1 | Leadership | Unemployed | 33 | 3.98 |
194 | 1 | Leadership | Full Time | 22 | 3.93 |
195 | 1 | Leadership | Unemployed | 27 | 3.41 |
196 | 1 | Leadership | Unemployed | 33 | 3.43 |
197 | 1 | Leadership | Unemployed | 36 | 3.7 |
198 | 1 | Leadership | Unemployed | 34 | 3.76 |
199 | 1 | Leadership | Unemployed | 55 | 3.9 |
200 | 1 | Leadership | Full Time | 33 | 3.23 |
Null hypothesis: H0: The true proportion of students of MBA program who dont declare a major is less than or equal to 0.5. .
Alternate hypothesis: Ha: The true proportion of students of MBA program who dont declare a major is greater than 0.5. .
Appropriate test, assumptions and conditions:
The appropriate test for testing the population proportion of a single population is Z-test for proportion. The assumptions required for this test are
i) The samples are independent and random.
ii) The samples are drawn from normal population
The conditions to be satisfied for this test are
and
Here n is the sample size and is the sample proportion. Here the number of students not declared major in the 200 students is 61. So the sample proportion is 61/200 = 0.305
The assumptions and conditions for this test are met and satisifed.
Test statistic:
The test statistic for the single proportion is
Substitute the respective values in the above test statistic
Level of significance and critical value
The level of significance for this test is 0.05 and the test is right tailed test. The right critical value at 5% level of significance is 1.6449. If the observed test statistic value exceeds this value, the null hypothesis can be rejected.
Conclusion:
Here the observed test statistic is -5.52 and it does not exceed the right critical value 1.6449. So we have no sufficient evidence against the null hypothesis and can conclude that the population proportion of the students who declare no major for the MBA program is not greater than 0.5.