Find the mean score and confidence interval

Question

Discuss the following:

Q: Problem concerns course scores (on a scale from 0-100) for a large undergraduate computer-programming course. The class is composed of both underclassmen (freshmen and sophomores) and upperclassmen (juniors and seniors). Also, the students are categorized according to their previous mathematical background from previous courses as 'low' or 'high' mathematical background. The variables in the excel file are:

- Score: On a scale from 0 - 100

- UpperCI: 1 for upperclassmen, 0 for underclassmen

- HighMath: 1 for high mathematical background, 0 otherwise

For the questions below, assume the data in file Course_Scores.xls represent a random sample for all college students. Answer the following questions:

a. Find the mean score and 95% confidence interval for all students

b. Find the mean score and 95% confidence interval for all upperclassmen

c. Find the mean score and 95% confidence interval for all upperclassmen with high math background

d. The professor of this course believes he has enough evidence to prove the hypothesis that upperclassmen score at least 5 points better, on average, than underclassmen. Do you agree with this statement? Conduct a test at the ± = .05 level of significance.

e. If we consider a good grade to be a score of 80 or above, is there enough evidence to reject the null hypothesis that the fraction of good grades is the same from low math backgrounds as those with high math backgrounds? Conduct a test at the ± = .05 level of significance.

f. Perform a similar test as in part e, but instead of math background, compare upperclassmen to underclassmen

Scores for a computer programming course
Student	Score	UpperCl	HighMath
1	90	0	1
2	54	0	0
3	56	0	1
4	61	0	1
5	73	1	1
6	81	0	1
7	66	1	1
8	74	0	1
9	71	0	1
10	60	1	0
11	85	1	1
12	44	1	0
13	53	0	1
14	98	1	1
15	61	1	1
16	73	0	0
17	69	0	0
18	81	0	1
19	72	1	1
20	68	0	0
21	78	1	1
22	80	0	0
23	36	1	0
24	59	1	1
25	87	1	1
26	70	0	1
27	79	1	1
28	76	1	1
29	57	0	0
30	81	0	1
31	75	0	0
32	68	1	1
33	75	1	0
34	86	1	1
35	62	0	1
36	61	0	0
37	73	1	0
38	39	1	1
39	82	1	1
40	75	1	1
41	53	1	1
42	74	1	1
43	65	1	0
44	91	0	1
45	76	0	1
46	89	0	1
47	79	1	1
48	74	1	0
49	60	1	0
50	80	0	1
51	94	1	1
52	75	0	0
53	65	0	1
54	64	1	1
55	69	1	0
56	39	0	0
57	72	0	1
58	70	1	1
59	68	1	1
60	74	1	1
61	62	1	0
62	70	1	0
63	45	1	0
64	83	1	1
65	92	1	1
66	71	0	1
67	68	0	1
68	79	1	0
69	89	1	1
70	68	1	0
71	82	1	0
72	54	0	1
73	56	0	0
74	95	0	1
75	69	1	0
76	80	0	1
77	81	0	1
78	82	1	1
79	77	1	0
80	69	1	1
81	65	1	0
82	68	1	0
83	56	1	0
84	62	0	0
85	72	1	1
86	70	0	0
87	82	1	1
88	74	0	0
89	79	1	1
90	56	1	0
91	69	1	0
92	74	1	1
93	64	1	1
94	83	1	1
95	83	0	1
96	66	0	1
97	83	1	1
98	86	1	1
99	56	1	0
100	58	0	1
101	79	0	1
102	100	1	1
103	75	1	1
104	75	1	1
105	43	0	0
106	64	0	1
107	71	0	1
108	85	1	0
109	71	1	1
110	88	0	1
111	65	1	0
112	72	0	0
113	60	1	0
114	74	1	0
115	83	0	0
116	77	1	0
117	67	1	1
118	77	0	0
119	70	1	1
120	48	1	1
121	79	0	1
122	77	1	0
123	72	0	0
124	96	0	1
125	62	1	0
126	70	1	0
127	74	1	0
128	73	0	0
129	92	1	1
130	65	1	0
131	62	1	0
132	77	0	0
133	89	1	1
134	76	1	1
135	79	1	1
136	56	1	1
137	66	1	1
138	94	0	1
139	77	1	1
140	75	1	1
141	67	1	0
142	74	1	1
143	67	0	0
144	59	0	0
145	71	0	1
146	76	1	1
147	78	1	0
148	70	0	1
149	62	0	0
150	72	1	0
151	65	1	0
152	64	0	0
153	60	0	0
154	75	1	0
155	69	0	1
156	88	0	1
157	80	1	0
158	68	1	0
159	71	1	1
160	79	0	1
161	74	0	1
162	71	1	1
163	68	0	0
164	76	1	0
165	75	1	1
166	65	0	0
167	66	0	1
168	68	1	1
169	74	1	0
170	80	0	0
171	58	1	0
172	79	0	1
173	62	1	1
174	72	1	0
175	63	0	1
176	75	1	1
177	73	1	0
178	75	1	1
179	72	0	1
180	69	0	1
181	83	1	0
182	77	0	0
183	60	0	0
184	51	1	1
185	65	0	1
186	69	0	1
187	60	1	0
188	74	1	1
189	84	1	1
190	84	1	1