Data for class STA-201: Principles of Statistics SEP2021 has been provided. For the questions below use the cluster sample method, developing a sample size of 28. It has been determined that there was a strong positive correlation between height and hand size. It has also been determined that there was not a statistical difference between how long a student has slept and how long they spent on homework. Verify these hypothesis in the questions below.

Table

ID	School Enrolled	Months Enrolled	Birthday Month	Distance to Work (whole miles)	Height (whole inches)	Foot Size (whole inches)	Hand Size (whole inches)	Sleep (minutes)	Homework (minutes)
1	Arts and Sciences	12	January	0	60	8	5	360	30
2	Applied Science and Technology	6	February	0	62	7	6	400	45
3	Business and Management	8	April	5	66	10	7	420	60
4	Nursing	10	June	10	68	12	8	440	15
5	Public Service	48	July	15	68	14	8	540	75
6	Arts and Sciences	48	June	30	70	12	9	480	120
7	Applied Science and Technology	36	October	32	72	11	8	320	80
8	Applied Science and Technology	32	November	36	75	14	7	440	60
9	Arts and Sciences	1	January	0	62	8	7	420	120
10	Arts and Sciences	1	June	8	67	10	7	480	180
11	Applied Science and Technology	12	February	12	60	12	8	360	60
12	Applied Science and Technology	1	August	25	72	11	8	400	120
13	Applied Science and Technology	12	November	6	63	7	5	480	120
14	Applies Science and Technology	49	August	7	72	12	8	360	55
15	Applied Science and Technology	6	November	29	72	11	8	375	150
16	Arts and Sciences	40	January	10	67	10	7	420	60
17	Applied Science and Technology	13	February	14	69	12	7	300	120
18	Applied Science and Technology	10	December	40	78	12	8	540	90
19	Applied Science and Technology	49	July	0	74	11	8	480	120
20	Applied Science and Technology	12	November	30	77	14	10	420	60
21	Applied Science and Technology	1	August	10	68	12	8	420	180
22	Arts and Sciences	9	July	2	71	11	7	360	90
23	Applied Science and Technology	24	April	15	71	10	7	420	180
24	Applied Science and Technology	9	November	83	71	11	7	420	90
25	Applied Science and Technology	4	January	5	74	13	8	360	120
26	Applied Science and Technology	7	June	53	70	12	7	390	120
27	Arts and Sciences	1	September	100	74	11	8	360	30
28	Arts and Sciences	36	December	17	67	8	7	360	120
29
30

Analyze the data and determine if there is any correlation relationship between the height of a person and the size of their hands. Also, using the t-test, make a comparison on whether more students in this class sleep longer than more(greater than or equal to 400 minutes) or less (less than 400 minutes) distributed between how long they spend on homework.

The first question you will address is if there is a relationship between a person's height and the size of their hands. A hypothesize has been made stating that there is a correlation between a person's height and the size of their hands. For this you will assume the null hypothesis of: if a person's height rises, their hand size also rise. The alternate hypothesis is: if a person's height rises there is not change in or there is a shrinking of the hand size. Break up the hand data to analysis the comparison individually. Provide graphs below that show the data broken up