Question

Is it true that students tend to gain weight during their first year in college? Cornell Professor of Nutrition David Levitsky recruited students from two large sections of an introductory health course. Although they were volunteers, they appeared to match the rest of the freshman class in terms of demographic variables such as sex and ethnicity. The students were weighed during the first week of the semester, then again 12 weeks later at the end of the semester (weights are in pounds).

subject	initial weight	terminal weight
1	171	168
2	110	111
3	134	136
4	115	119
5	150	155
6	104	106
7	142	148
8	120	124
9	144	148
10	156	154
11	114	114
12	121	123
13	122	126
14	120	115
15	115	118
16	110	113
17	142	146
18	127	127
19	102	105
20	125	125
21	157	158
22	119	126
23	113	114
24	120	128
25	135	139
26	148	150
27	110	112
28	160	163
29	220	224
30	132	133
31	145	147
32	141	141
33	158	160
34	135	134
35	148	150
36	164	165
37	137	138
38	198	201
39	122	124
40	146	146
41	150	151
42	187	192
43	94	96
44	105	105
45	127	130
46	142	144
47	140	143
48	107	107
49	104	105
50	111	112
51	160	162
52	134	134
53	151	151
54	127	130
55	106	108
56	185	188
57	125	128
58	125	126
59	155	158
60	118	120
61	149	150
62	149	149
63	122	121
64	155	158
65	160	161
66	115	119
67	167	170
68	131	131

1) Construct a dotplot depicting the distribution of the change in the students’ weights from the beginning of the semester to the end of the semester.

2)Suppose Professor Levitsky wishes to use the data he collected from his students in a research paper. He wants to prove freshman students tend to gain weight during their first semester in college.

Frame this research question as a hypothesis testing problem. Identify the parameter being tested, the null value, and explicitly write out the null and alternative hypothesis in terms of the parameter and null value.

Answer 1

1. The dot plots are:

2. The hypothesis being tested is:

H0: µ1 = µ2

H1: µ1 < µ2

136.074	mean initial weight
137.985	mean terminal weight
-1.912	mean difference (initial weight - terminal weight)
2.128	std. dev.
0.258	std. error
68	n
67	df
-7.407	t
2.81E-10	p-value (two-tailed)

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that freshman students tend to gain weight during their first semester in college.