Question

1. The data set on sheet #1 gives data on GPA category and number of hours studied. Construct comparative box plots of the data first GPA category. Then conduct two-sample t-test on the data for whether GPA category influences the number of hours studied. Be prepared to explain the results of the test and the meaning of the boxplots and how they relate to each other. Then redo the analysis by replacing the ordinal GPA category with a numerical dummy variable with Low=0, High=1. Run a regression analysis on how study hours (x) influence GPA category (y). Include the scatterplot. Compare the results of the two tests. Be able to state and null and alternative hypotheses

Student	GPA	Hours per week
1	Low	6
2	Low	18
3	Low	16
4	Low	14
5	High	0
6	Low	22
7	Low	15
8	Low	12
9	High	6
10	Low	7
11	Low	5
12	High	20
13	High	9
14	High	9
15	Low	22
16	Low	23
17	High	8
18	Low	7
19	Low	14
20	Low	12
21	Low	0
22	High	7
23	High	4
24	Low	9
25	Low	0
26	Low	0
27	High	6
28	High	14
29	Low	10
30	Low	9
31	High	5
32	High	7
33	High	4
34	High	16
35	High	0
36	Low	20
37	Low	13
38	High	0
39	High	4
40	Low	6
41	Low	17
42	Low	8
43	High	4
44	Low	0
45	High	16
46	Low	17
47	Low	4
48	High	11
49	Low	14
50	Low	16
51	High	11
52	High	7
53	High	4
54	Low	11
55	Low	8
56	High	2
57	Low	0
58	Low	0
59	High	13
60	Low	18
61	Low	28
62	High	1
63	Low	20
64	Low	13
65	Low	4
66	Low	7
67	High	11
68	Low	12
69	High	5
70	Low	7
71	Low	22
72	High	8
73	Low	19
74	Low	8
75	High	2
76	High	11
77	Low	18
78	Low	20
79	High	7
80	High	4
81	High	4
82	High	16
83	High	15
84	Low	9
85	High	8
86	High	10
87	Low	13
88	High	9
89	Low	2
90	Low	22
91	Low	12
92	High	6
93	High	9
94	Low	20
95	Low	14
96	High	7
97	High	15
98	High	9
99	High	2
100	Low	23

Answer 1

Box plot:

we can observe that, Mean number of hours studied by GPA-Low students is greater than Mean number of hours studied by GPA-high students. Now we need to test this statement using 2 sample t-test.

2 sample t-test:

Null hypothesis Ho: There is no difference in mean number of hours studied by GPA-Low students and mean number of hours studied by GPA-High students.

Alternative hypothesis H1: Mean number of hours studied by GPA-Low students is greater than Mean number of hours studied by GPA-high students.

(So this is a right tailed or one tailed test)

Test statistic:

where

By usual definition of mean and standard deviation we get,

Substituting the above values in test statistic equation we get,

t=3.511

and degrees of freedom

Now to draw the conclusion, we need to compare the t value (3.511) with t-distribution value at 5% level of significance () with degrees of freedom 98. (its called critical value)

i.e from t-distibution table we get

Since , we reject the null hypothesis at 5% level of significance.

Which means "Mean number of hours studied by GPA-Low students is greater than Mean number of hours studied by GPA-high students."

Or

"GPA category influence the number of hours studied"

Scatter Plot:

we can observe from above Scatter plot that, there is no linear relationship between, Number of hours studied and GPA category. Since dependent variable GPA category is binary (o or 1) we can try to fit a logistic regression.

Logistic regression Model:

Logistic regression model is given by,

and we get the model,