Question

StudentNO	Gender	Height in inchese
1	Female	63
2	Female	64.0
3	Male	67.0
4	Female	59
5	Male	60
6	Female	61
7	Female	62
8	Female	63
9	Female	63
10	Female	64
11	Male	64
12	Female	65
13	Female	65
14	Female	65
15	Female	65
16	Female	66
17	Female	66
18	Male	67
19	Male	67
20	Male	67
21	Female	67
22	Male	67
23	Male	67
24	Female	67.5
25	Male	68
26	Female	68
27	Male	68
28	Male	68
29	Female	68
30	Female	68
31	Female	69
32	Female	69
33	Female	69
34	Male	69
35	Male	69
36	Male	69
37	Female	69
38	Male	69
39	Male	69
40	Female	60.0
41	Male	70
42	Male	70
43	Male	70
44	Female	70
45	Male	70
46	Male	70
47	Male	70
48	Female	70
49	Female	70
50	Male	70
51	Male	70
52	Male	70
53	Male	71
54	Male	71
55	Male	71
56	Male	71
57	Male	71
58	Male	71
59	Male	71
60	Male	71
61	Male	72
62	Male	72
63	Male	72
64	Male	72
65	Male	72
66	Male	72
67	Male	73
68	Male	73
69	Male	73
70	Male	73
71	Male	73
72	Male	73
73	Male	74
74	Male	74
75	Male	75
76	Male	75
77	Male	75
78	Male	75
79	Male	75
80	Male	76
81	Male	76
82	Male	78
83	Male	78

Data collected to understand the height differences between male and female college students at University of Cincinnati. While it is impossible to have a population data, a sample data was collected from ENED3066 summer 2020. The data is available through: data above.

Use the collected data, run appropriate hypothesis testing to predict the height information for male and female students at UC.

1: If we assume the variances of the height for both male and female students are unknow, what is the degree of freedom for the hypothesis test assuming unequal variance?

2: Suppose our null hypothesis is that there is no differences in heights between male and female students at UC. The alternative hypothesis is there is differences. Assuming equal variances, what is the test static value, t value? keep two numbers after decimal points

3: Suppose our null hypothesis is that there is no differences in heights between male and female students at UC. The alternative hypothesis is there is differences. Given α=0.05, should you reject the null hypothesis?

4: Suppose our null hypothesis is that there is no differences in heights between male and female students at UC. The alternative hypothesis is the height of the male students is greater than the female students. Given α=0.05, what is t critical value of the test assuming equal variance? keep two decimal spaces

5: Suppose our null hypothesis is that there is no differences in heights between male and female students at UC. The alternative hypothesis is the height of the male students is greater than the female students. Given α=0.05, what is Z critical value of the test assuming normality? keep two decimal spaces

Answer 1

1. df = 53

2. t = 6.82

3. Yes, p-value = 0.0000

4. t-crit = 1.66

5. z-crit = 1.64

Female	Male
63	67
64	60
59	64
61	67
62	67
63	67
63	67
64	67
65	68
65	68
65	68
65	69
66	69
66	69
67	69
67.5	69
68	70
68	70
68	70
69	70
69	70
69	70
69	70
60	70
70	70
70	71
70	71
	71
	71
	71
	71
	71
	71
	72
	72
	72
	72
	72
	72
	73
	73
	73
	73
	73
	73
	74
	74
	75
	75
	75
	75
	75
	76
	76
	78
	78