Question

In: Statistics and Probability

You have heard from idle chatter that most students don't declare a major in their MBA...

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

Solutions

Expert Solution

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.

orchestra answered 1 year ago
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