Question

Is there a difference between the means of occupancy rates in May and August? Answer your question by calculating an approximate and appropriate symmetric 95% confidence interval using a Z statistic. Explain your findings

OR_MAY	OR_AUG
60	97
86	99
93	99
89	96
74	90
81	84
83	99
71	99
90	98
83	97
77	99
82	97
90	98
81	98
20	90
87	95
48	94
60	96
45	98
80	95
65	91
60	95
75	90
15	70
16	66
97	100
74	94
62	97
40	85
82	97
24	76
49	98
16	93
60	86
42	73
68	87
55	86
75	93
35	95
0	95
40	80
40	40
10	80
83	90
50	100
77	98
81	99
37	96
27	90
49	96
53	98
60	97
80	100
58	95
64	93
65	100
68	98
75	100
55	84
60	95
56	96
10	100
85	95
4	77
24	92
85	98
75	92
44	84
45	95
0	70
34	92
35	95
70	98
65	99
15	90
40	100
10	90
10	90
35	70
50	100
2	95
0	80
3	90
30	90
15	80
83	95
91	99
85	100
80	90
50	100
79	94
92	98
87	99
84	97
65	98
86	94
62	92
70	95
87	97
87	99
50	97
61	97
59	99
77	100
46	95
81	94
48	98
15	98
80	100
52	99
90	97
90	99
75	90
20	100
10	90
30	100
53	99
52	99
90	97
53	92
48	98
84	96
90	97
35	98
25	95
35	100
10	95
10	90
60	100
70	92
3	78
10	90
10	90
75	100
10	70

Answer 1

Since , the formula to find Confidence Interval of a sample is given by -

where ,

for 95% confidence interval .

is the sample mean and is the standard deviation of the given sample .

So let us first calculate standard deviation of the given sample , which is given by -

We have for data of month May -

Mean , = 54.05 . Therefore we have -

OR_MAY xi	OR_AUG yi
60	97	35.4
86	99	1020.8
93	99	1517.1
89	96	1221.5
74	90	398
81	84	726.3
83	99	838.1
71	99	287.3
90	98	1292.4
83	97	838.1
77	99	526.7
82	97	781.2
90	98	1292.4
81	98	726.3
20	90	1159.4
87	95	1085.7
48	94	36.6
60	96	35.4
45	98	81.9
80	95	673.4
65	91	119.9
60	95	35.4
75	90	438.9
15	70	1524.9
16	66	1447.8
97	100	1844.7
74	94	398
62	97	63.2
40	85	197.4
82	97	781.2
24	76	903
49	98	25.5
16	93	1447.8
60	86	35.4
42	73	145.2
68	87	194.6
55	86	0.9
75	93	438.9
35	95	362.9
0	95	2921.4
40	80	197.4
40	40	197.4
10	80	1940.4
83	90	838.1
50	100	16.4
77	98	526.7
81	99	726.3
37	96	290.7
27	90	731.7
49	96	25.5
53	98	1.1
60	97	35.4
80	100	673.4
58	95	15.6
64	93	99
65	100	119.9
68	98	194.6
75	100	438.9
55	84	0.9
60	95	35.4
56	96	3.8
10	100	1940.4
85	95	957.9
4	77	2505
24	92	903
85	98	957.9
75	92	438.9
44	84	101
45	95	81.9
0	70	2921.4
34	92	402
35	95	362.9
70	98	254.4
65	99	119.9
15	90	1524.9
40	100	197.4
10	90	1940.4
10	90	1940.4
35	70	362.9
50	100	16.4
2	95	2709.2
0	80	2921.4
3	90	2606.1
30	90	578.4
15	80	1524.9
83	95	838.1
91	99	1365.3
85	100	957.9
80	90	673.4
50	100	16.4
79	94	622.5
92	98	1440.2
87	99	1085.7
84	97	897
65	98	19.9
86	94	1020.8
62	92	63.2
70	95	254.4
87	97	1085.7
87	99	1085.7
50	97	16.4
61	97	48.3
59	99	24.5
77	100	526.7
46	95	64.8
81	94	726.3
48	98	36.6
15	98	1524.9
80	100	673.4
52	99	4.2
90	97	1292.4
90	99	1292.4
75	90	438.9
20	100	1159.4
10	90	1940.4
30	100	578.4
53	99	1.1
52	99	4.2
90	97	1292.4
53	92	1.1
48	98	36.6
84	96	897
90	97	1292.4
35	98	362.9
25	95	843.9
35	100	362.9
10	95	1940.4
10	90	1940.4
60	100	35.4
70	92	254.4
3	78	2606.1
10	90	1940.4
10	90	1940.4
75	100	438.9
10	70	1940.4

Thus ,

Standard deviation = 27.6779

Mean = 54.05

Therefore, from (1);

Similarly , standard deviation of data of month august = 858.819595

Mean , = 167.87

Therefore ,

From (1)

Thus, from the two confidence intervals , we can say that the occupancy rate in may lies between ( 49.35 , 58.75 ) and that in june lies between ( 21.91 , 313.83 )

Thus , there is a difference between the two occupancy rates of two months . The OR in June has more wide range than that in May .