You are a registered nurse working in a weight loss clinic, and you have collected data on weight loss achieved by your clients who have undertaken various diets over a 6-week period. You collected background data on sex (0=females, 1=males), weight at the start of the diet (pre_wt, kg), weight at the end of 6 weeks (post_wt, kg), and other demographic variables. The complete data set is in the Data folder in A2L Contents, is called Q8_DIET. Note that the data set has some missing data (sex is missing for first 2 observations), as commonly occurs in the real world. Use these data to answer the questions below.

Conduct the appropriate statistical test to determine whether weight loss is the same in females and males. Assume that weight loss is normally distributed with equal variance in both sexes, and = 0.05. Show all calculations.

Calculate the 95% confidence interval for the mean difference in weight loss between the sexes. Show your calculation.

Calculate the 99% confidence interval for the mean difference in weight loss between the sexes. Show your calculation.

ID	sex	age	heigh	pre_wt	diet	post_wt	Weight_difference
25		41	171	60	2	60	0
26		32	174	103	2	103	0
1	0	22	159	58	1	54.2	3.8
2	0	46	192	60	1	54	6
3	0	55	170	64	1	63.3	0.700000000000003
4	0	33	171	64	1	61.1	2.9
5	0	50	170	65	1	62.2	2.8
6	0	50	201	66	1	64	2
7	0	37	174	67	1	65	2
8	0	28	176	69	1	60.5	8.5
9	0	28	165	70	1	68.1	1.90000000000001
10	0	45	165	70	1	66.9	3.09999999999999
11	0	60	173	72	1	70.5	1.5
12	0	48	156	72	1	69	3
13	0	41	163	72	1	68.4	3.59999999999999
14	0	37	167	82	1	81.1	0.900000000000006
27	0	44	174	58	2	60.1	-2.1
28	0	37	172	58	2	56	2
29	0	41	165	59	2	57.3	1.7
30	0	43	171	61	2	56.7	4.3
31	0	20	169	62	2	55	7
32	0	51	174	63	2	62.4	0.600000000000001
33	0	31	163	63	2	60.3	2.7
34	0	54	173	63	2	59.4	3.6
35	0	50	166	65	2	62	3
36	0	48	163	66	2	64	2
37	0	16	165	68	2	63.8	4.2
38	0	37	167	68	2	63.3	4.7
39	0	30	161	76	2	72.7	3.3
40	0	29	169	77	2	77.5	-0.5
52	0	51	165	60	3	53	7
53	0	35	169	62	3	56.4	5.6
54	0	21	159	64	3	60.6	3.4
55	0	22	169	65	3	58.2	6.8
56	0	36	160	66	3	58.2	7.8
57	0	20	169	67	3	61.6	5.4
58	0	35	163	67	3	60.2	6.8
59	0	45	155	69	3	61.8	7.2
60	0	58	141	70	3	63	7
61	0	37	170	70	3	62.7	7.3
62	0	31	170	72	3	71.1	0.900000000000006
63	0	35	171	72	3	64.4	7.59999999999999
64	0	56	171	73	3	68.9	4.09999999999999
65	0	48	153	75	3	68.7	6.3
66	0	41	157	76	3	71	5
15	1	39	168	71	1	71.6	-0.599999999999994
16	1	31	158	72	1	70.9	1.09999999999999
17	1	40	173	74	1	69.5	4.5
18	1	50	160	78	1	73.9	4.09999999999999
19	1	43	162	80	1	71	9
20	1	25	165	80	1	77.6	2.40000000000001
21	1	52	177	83	1	79.1	3.90000000000001
22	1	42	166	85	1	81.5	3.5
23	1	39	166	87	1	81.9	5.09999999999999
24	1	40	190	88	1	84.5	3.5
41	1	51	191	71	2	66.8	4.2
42	1	38	199	75	2	72.6	2.40000000000001
43	1	54	196	75	2	69.2	5.8
44	1	33	190	76	2	72.5	3.5
45	1	45	160	78	2	72.7	5.3
46	1	37	194	78	2	76.3	1.7
47	1	44	163	79	2	73.6	5.40000000000001
48	1	40	171	79	2	72.9	6.09999999999999
49	1	37	198	79	2	71.1	7.90000000000001
50	1	39	180	80	2	81.4	-1.40000000000001
51	1	31	182	80	2	75.7	4.3
67	1	36	155	71	3	68.5	2.5
68	1	47	179	73	3	72.1	0.900000000000006
69	1	29	166	76	3	72.5	3.5
70	1	37	173	78	3	77.5	0.5
71	1	31	177	78	3	75.2	2.8
72	1	26	179	78	3	69.4	8.59999999999999
73	1	40	179	79	3	74.5	4.5
74	1	35	183	83	3	80.2	2.8
75	1	49	177	84	3	79.9	4.09999999999999
76	1	28	164	85	3	79.7	5.3
77	1	40	167	87	3	77.8	9.2
78	1	51	175	88	3	81.9	6.09999999999999