Question

The research team would like to estimate the average gender difference in age.

Compute a 90% estimate and confidence interval for the difference in the average age of Female and Male employees.

What is the margin of error of the confidence interval ? (Use 3 decimals)

Employee Number1	Annual Salary	Gender	Age (years)	Experience (years)	Training Level
1	$     32,368	F	42	3	B
2	$     53,174	M	54	10	B
3	$     52,722	M	47	10	A
4	$     53,423	M	47	1	B
5	$     50,602	M	44	5	B
6	$     49,033	M	42	10	A
7	$     24,395	M	30	5	A
8	$     24,395	F	52	6	A
9	$     43,124	M	48	8	A
10	$     23,975	F	58	4	A
11	$     53,174	M	46	4	C
12	$     58,515	M	36	8	C
13	$     56,294	M	49	10	B
14	$     49,033	F	55	10	B
15	$     44,884	M	41	1	A
16	$     53,429	F	52	5	B
17	$     46,574	M	57	8	A
18	$     58,968	F	61	10	B
19	$     53,174	M	50	5	A
20	$     53,627	M	47	10	B
21	$     49,033	M	54	5	B
22	$     54,981	M	47	7	A
23	$     62,530	M	50	10	B
24	$     27,525	F	38	3	A
25	$     24,395	M	31	5	A
26	$     56,884	M	47	10	A
27	$     52,111	M	56	5	A
28	$     44,183	F	38	5	B
29	$     24,967	F	55	6	A
30	$     35,423	F	47	4	A
31	$     41,188	F	35	2	B
32	$     27,525	F	35	3	A
33	$     35,018	M	39	1	A
34	$     44,183	M	41	2	A
35	$     35,423	M	44	1	A
36	$     49,033	M	53	8	A
37	$     40,741	M	47	2	A
38	$     49,033	M	42	10	A
39	$     56,294	F	44	6	C
40	$     47,180	F	45	5	C
41	$     46,574	M	56	8	A
42	$     52,722	M	38	8	C
43	$     51,237	M	58	2	B
44	$     53,627	M	52	8	A
45	$     53,174	M	54	10	A
46	$     56,294	M	49	10	B
47	$     49,033	F	53	10	B
48	$     49,033	M	43	9	A
49	$     55,549	M	35	8	C
50	$     51,237	M	56	1	C
51	$     35,200	F	38	1	B
52	$     50,175	F	42	5	A
53	$     24,352	F	35	1	A
54	$     27,525	F	40	3	A
55	$     29,606	F	34	4	B
56	$     24,352	F	35	1	A
57	$     47,180	F	45	5	B
58	$     49,033	M	54	10	A
59	$     53,174	M	47	10	A
60	$     53,429	F	45	7	B
61	$     53,627	M	47	10	A
62	$     26,491	F	46	7	A
63	$     42,961	M	36	3	B
64	$     53,174	M	45	5	A
65	$     36,292	M	46	0	A
66	$     37,292	M	47	1	A
67	$     41,188	F	34	3	B
68	$     57,242	F	45	7	C
69	$     53,429	F	44	6	C
70	$     53,174	M	50	10	B
71	$     44,138	F	38	2	B

Answer 1

	F	M
	42	54
	52	47
	58	47
	55	44
	52	42
	61	30
	38	48
	38	46
	55	36
	47	49
	35	41
	35	57
	44	50
	45	47
	53	54
	38	47
	42	50
	35	31
	40	47
	34	56
	35	39
	45	41
	45	44
	46	53
	34	47
	45	42
	44	56
	38	38
		58
		52
		54
		49
		43
		35
		56
		54
		47
		47
		36
		45
		46
		47
		50
mean	43.96429	46.55814
sd	7.805421	6.877508
n	28	43

M₁ & M₂ = sample means
t = t statistic determined by confidence level
s_{(M1 - M2)} = standard error = √((s²_p/n₁) + (s²_p/n₂))

μ₁ - μ₂ = (M₁ - M₂) ± ts_{(M1 - M2)}

margin or error = ts_{(M1 - M2)}

Calculation

Pooled Variance
s²_p = ((df₁)(s²₁) + (df₂)(s²₂)) / (df₁ + df₂) = 3631.57 / 69 = 52.63

Standard Error
s_{(M1 - M2)} = √((s²_p/n₁) + (s²_p/n₂)) = √((52.63/28) + (52.63/43)) = 1.76

Margin of error

= 1.67 * 1.76 = 2.9392

Confidence Interval
μ₁ - μ₂ = (M₁ - M₂) ± ts_{(M1 - M2)} = 2.5939 ± (1.67 * 1.76) = 2.5939 ± 2.9372187