You have been appointed by the Ministry of Manpower to analyse the private-MNC and private-SME pay gap in Singapore/Malaysia. The data are drawn from the 2018/2019 survey. Using the tools learned in your current Business Statistics course provide the ministry with an analysis of the MNC-SME pay gap. You may assume the officers at the ministry have a good understanding of basic statistics. In addition, the ministry would like you to prepare a ministerial brief to illustrate the key findings of your analysis to the Minister for Manpower. Answer each of the following questions, showing your analysis in detail (Excel), and use it in your report. Use the 5% significance level and the 95% confidence level where relevant. 1. Focusing on the variable wage for the MNC sector employees only for this question: as shown in several lectures there are two distinct methods of calculating summary or descriptive statistics using Excel. This question requires you to use both methods. First use Excel Data Analysis Tool Pack (the descriptive statistics option) to calculate and interpret the summary statistics. Second use Excel to calculate all descriptive statistics documented in your report. These calculations should be carefully laid out in Excel and should NOT use any hard-wired Excel statistical functions e.g. Average, Median, Mode, STDEV et al. You can use the Excel sort command, the sum command, and any other non-statistical Excel commands. 2. Repeat step 1 above for the variable wage for the SME sector employees. 3. Draw a histogram of the wage distribution for the MNC and SME sector employees respectively. Interpret the graphs carefully. 4. What are the main differences in demographic and social-economic characteristics between employees in the MNC and SME sector? Aid your answer with appropriate tables/graphs. 5. Propose a statistical method to estimate the mean hourly wage rate for all MNC sector employees and all SME sector employees, respectively. Clearly label your diagram and indicate any assumptions made and explain carefully. 6. A media report claims that the mean hourly wage rate for all MNC sector employees in was $ 49. Do you agree? Perform a hypothesis test at the 5% significance level. Clearly label your diagram and indicate any assumptions made. Explain carefully if any potential errors in your decision making.

Just need question 4, 5 and 6 answers based on the data provided below

Below is question 1-3 answers

SME

gender	age	wage	degree	married	(wage) x- x	(x - x)^2
Male	36	3.01	Yes	Yes	-34.49	1189.81
Male	61	6.52	No	No	-30.98	959.82
Female	25	9.20	No	No	-28.30	801.04
Female	22	10.00	No	No	-27.50	756.40
Male	23	10.56	No	No	-26.94	725.91
Female	27	13.50	Yes	No	-24.00	576.13
Female	27	14.58	No	Yes	-22.92	525.30
Male	21	16.27	No	No	-21.24	450.97
Male	21	16.43	No	No	-21.07	444.12
Female	31	17.50	No	No	-20.00	400.11
Male	27	18.00	No	No	-19.50	380.35
Female	41	18.20	Yes	Yes	-19.30	372.59
Female	26	18.34	No	Yes	-19.16	367.13
Female	31	19.18	No	No	-18.32	335.72
Female	23	19.18	No	No	-18.32	335.65
Female	28	19.67	No	Yes	-17.83	317.85
Female	63	19.91	No	No	-17.60	309.63
Male	24	19.98	No	No	-17.52	306.93
Male	52	20.00	No	No	-17.50	306.34
Female	27	20.18	Yes	No	-17.32	299.93
Female	27	20.83	No	Yes	-16.67	277.87
Female	49	21.00	No	Yes	-16.50	272.34
Male	47	21.40	No	No	-16.10	259.30
Female	43	21.42	Yes	No	-16.08	258.70
Female	31	21.49	Yes	No	-16.01	256.44
Female	27	21.50	Yes	Yes	-16.00	256.09
Male	27	21.82	No	No	-15.68	246.00
Female	60	21.90	No	No	-15.60	243.29
Male	52	22.00	No	No	-15.50	240.33
Male	22	22.28	No	No	-15.23	231.88
Male	22	22.50	No	No	-15.00	225.08
Male	60	22.63	No	No	-14.87	221.15
Female	41	22.64	No	Yes	-14.86	220.85
Male	39	23.08	No	No	-14.42	208.01
Female	39	24.56	No	Yes	-12.94	167.51
Female	48	24.57	No	Yes	-12.93	167.22
Male	30	24.95	No	Yes	-12.55	157.57
Male	22	25.00	No	No	-12.50	156.32
Male	26	25.57	Yes	No	-11.94	142.47
Male	22	25.67	No	No	-11.84	140.09
Male	32	26.00	No	No	-11.50	132.31
Female	46	26.24	No	Yes	-11.26	126.85
Female	47	26.32	No	No	-11.19	125.15
Male	31	26.90	No	Yes	-10.60	112.32
Male	60	27.17	No	Yes	-10.34	106.83
Female	53	27.17	No	Yes	-10.34	106.83
Female	25	27.34	Yes	No	-10.16	103.27
Female	35	27.63	No	No	-9.88	97.57
Male	63	28.00	No	Yes	-9.50	90.30
Male	28	28.00	Yes	No	-9.50	90.30
Female	42	28.33	Yes	No	-9.17	84.08
Male	44	28.33	No	No	-9.17	84.08
Female	28	28.62	Yes	No	-8.88	78.90
Male	24	28.78	No	No	-8.73	76.17
Male	27	28.85	No	No	-8.65	74.87
Female	26	28.92	Yes	No	-8.58	73.64
Female	59	29.08	No	Yes	-8.42	70.89
Male	23	29.31	No	No	-8.19	67.13
Male	40	29.70	Yes	Yes	-7.80	60.92
Male	22	31.00	Yes	No	-6.50	42.28
Female	50	31.11	No	Yes	-6.39	40.85
Female	65	31.13	Yes	No	-6.38	40.67
Male	28	31.21	Yes	No	-6.29	39.61
Male	30	31.43	Yes	No	-6.07	36.89
Female	37	31.67	No	Yes	-5.84	34.06
Male	32	32.34	No	No	-5.16	26.61
Female	25	32.42	No	No	-5.08	25.82
Male	32	32.50	No	Yes	-5.00	25.03
Female	51	33.19	No	Yes	-4.32	18.63
Male	35	33.33	No	Yes	-4.17	17.38
Male	27	33.40	Yes	Yes	-4.10	16.83
Male	38	34.38	No	No	-3.13	9.78
Female	64	34.87	No	No	-2.63	6.92
Male	26	34.92	Yes	No	-2.58	6.67
Female	34	37.09	No	Yes	-0.41	0.17
Male	27	37.45	No	Yes	-0.06	0.00
Male	37	37.50	No	No	-0.00	0.00
Female	33	37.60	Yes	Yes	0.10	0.01
Male	23	38.16	No	No	0.66	0.43
Female	30	38.35	No	No	0.85	0.72
Male	37	38.35	No	No	0.85	0.72
Female	41	38.46	No	Yes	0.96	0.92
Female	27	38.80	No	No	1.30	1.68
Male	26	38.85	No	No	1.35	1.82
Male	35	39.00	Yes	Yes	1.50	2.24
Female	29	39.50	No	No	2.00	3.99
Female	55	39.85	Yes	No	2.35	5.51
Male	42	39.95	No	Yes	2.45	5.99
Female	22	40.00	No	No	2.50	6.24
Male	30	40.05	No	No	2.54	6.47
Female	61	41.67	Yes	No	4.16	17.34
Female	41	41.84	Yes	No	4.33	18.78
Male	29	42.44	No	No	4.94	24.40
Female	59	42.51	No	Yes	5.01	25.11
Male	37	43.02	No	No	5.52	30.47
Male	29	43.15	No	No	5.65	31.89
Male	46	43.16	Yes	No	5.66	32.01
Female	32	43.34	Yes	No	5.84	34.11
Male	50	43.86	No	Yes	6.36	40.41
Male	30	44.60	No	Yes	7.10	50.37
Male	33	44.76	No	No	7.25	52.60
Female	33	44.87	Yes	No	7.36	54.23
Male	40	46.02	No	No	8.52	72.55
Male	44	46.02	Yes	Yes	8.52	72.55
Male	26	46.42	Yes	No	8.92	79.54
Female	58	47.95	Yes	Yes	10.45	109.15
Female	31	48.08	No	No	10.57	111.77
Female	36	48.20	Yes	No	10.70	114.43
Female	46	48.90	Yes	No	11.40	129.90
Male	32	49.02	Yes	No	11.52	132.70
Male	55	50.93	Yes	No	13.43	180.26
Male	46	52.94	Yes	No	15.44	238.31
Male	37	56.25	Yes	No	18.75	351.46
Female	43	56.40	No	Yes	18.90	357.11
Male	64	57.53	No	Yes	20.02	400.89
Male	36	61.38	Yes	Yes	23.88	570.13
Male	36	61.50	No	No	24.00	575.87
Male	49	61.72	No	Yes	24.22	586.52
Male	31	68.95	Yes	Yes	31.44	988.77
Female	60	70.00	No	Yes	32.50	1056.08
Male	42	70.21	Yes	No	32.71	1069.95
Male	35	70.83	Yes	No	33.33	1110.93
Male	31	73.10	No	Yes	35.60	1267.17
Male	38	73.64	Yes	Yes	36.14	1305.91
Male	38	78.26	Yes	No	40.76	1661.16
Female	43	79.69	No	Yes	42.18	1779.41
Male	38	79.89	Yes	No	42.39	1796.59
Male	63	80.00	Yes	No	42.50	1806.02
Male	56	87.50	No	Yes	50.00	2499.73
Male	64	91.18	No	Yes	53.67	2880.88
Male	31	100.00	No	No	62.50	3905.92
Male	53	100.00	Yes	Yes	62.50	3905.92
Male	44	100.58	No	No	63.08	3978.93
		4987.85				52205.79

Sum of all Wages	4987.85
Count of Employees	133
Mean Wage	37.50
Median Wage	32.42
Mode	19.18, 27.17, 28.00, 28.33, 38.35, 46.02, 100.00
(X-)^2 / n-1	395.50
Standard Deviation	19.89

Column1
Mean	37.50266132
Standard Error	1.724433944
Median	32.42105
Mode	27.16667
Standard Deviation	19.8871424
Sample Variance	395.4984327
Kurtosis	1.503935369
Skewness	1.263652498
Range	97.572373
Minimum	3.009027
Maximum	100.5814
Sum	4987.853956
Count	133
	0

MNC

gender	age	wage	degree	married	(wage) x- x	(x - x)^2
Female	45	20.59	No	No	-23.14	535.66
Female	23	21.28	No	No	-22.46	504.31
Male	44	22.50	No	Yes	-21.24	451.06
Female	27	22.92	Yes	No	-20.82	433.53
Male	28	23.11	No	No	-20.63	425.72
Female	24	23.30	No	No	-20.44	417.90
Female	31	23.34	Yes	No	-20.40	416.08
Male	28	24.24	Yes	No	-19.50	380.30
Female	39	25.00	Yes	Yes	-18.74	351.12
Female	22	26.32	Yes	No	-17.42	303.54
Female	27	27.78	Yes	No	-15.96	254.73
Female	64	28.57	No	No	-15.17	230.03
Female	44	29.22	Yes	No	-14.52	210.71
Female	25	29.25	Yes	No	-14.49	209.91
Female	22	30.67	No	No	-13.07	170.86
Male	28	30.67	No	No	-13.07	170.86
Female	27	30.85	No	No	-12.89	166.10
Male	54	30.91	No	Yes	-12.83	164.58
Male	45	31.25	Yes	Yes	-12.49	155.95
Male	28	31.88	No	No	-11.86	140.73
Female	46	32.43	No	No	-11.31	127.82
Female	43	33.58	Yes	Yes	-10.16	103.29
Female	61	33.63	No	Yes	-10.11	102.28
Male	38	33.75	No	No	-9.99	99.76
Female	26	34.00	Yes	Yes	-9.74	94.83
Male	30	35.54	Yes	No	-8.20	67.20
Male	28	35.71	No	No	-8.02	64.38
Female	28	35.77	Yes	No	-7.97	63.50
Female	34	35.97	No	Yes	-7.76	60.29
Female	25	36.43	No	No	-7.30	53.36
Female	32	36.64	Yes	Yes	-7.09	50.32
Male	48	37.21	No	No	-6.53	42.61
Female	24	37.25	Yes	No	-6.48	42.05
Female	29	37.33	No	No	-6.40	41.02
Male	41	37.49	Yes	Yes	-6.25	39.05
Female	37	37.50	Yes	Yes	-6.24	38.91
Female	57	37.50	No	Yes	-6.24	38.91
Male	32	39.47	No	No	-4.26	18.19
Male	31	39.80	Yes	No	-3.94	15.51
Male	31	40.00	No	No	-3.74	13.97
Female	51	40.54	No	Yes	-3.20	10.22
Female	32	41.10	No	No	-2.64	6.98
Male	33	41.23	Yes	Yes	-2.51	6.32
Female	45	41.37	No	Yes	-2.37	5.62
Male	53	41.60	No	No	-2.14	4.57
Female	32	42.13	Yes	Yes	-1.61	2.58
Male	63	42.42	Yes	No	-1.31	1.73
Female	46	43.05	No	Yes	-0.69	0.47
Male	58	45.13	Yes	Yes	1.39	1.94
Male	30	45.94	Yes	Yes	2.20	4.85
Female	29	46.24	No	No	2.50	6.26
Male	46	47.50	No	No	3.76	14.15
Male	40	47.67	Yes	No	3.94	15.49
Female	52	47.71	Yes	No	3.97	15.78
Male	39	48.13	Yes	No	4.39	19.24
Male	65	49.47	No	Yes	5.74	32.90
Male	40	50.00	Yes	Yes	6.26	39.21
Male	57	50.00	No	No	6.26	39.21
Male	59	50.00	No	No	6.26	39.21
Male	26	50.35	Yes	Yes	6.61	43.72
Male	37	50.88	Yes	No	7.14	50.93
Female	31	51.35	No	Yes	7.61	57.96
Male	44	51.45	No	No	7.71	59.47
Male	44	52.50	No	No	8.76	76.77
Female	31	52.63	Yes	No	8.89	79.09
Female	31	52.75	Yes	Yes	9.01	81.21
Female	55	54.60	Yes	Yes	10.86	117.98
Female	41	55.56	No	No	11.82	139.65
Female	60	55.59	Yes	Yes	11.86	140.58
Female	31	55.67	Yes	Yes	11.93	142.29
Female	51	56.53	Yes	Yes	12.79	163.54
Male	39	57.14	Yes	No	13.40	179.69
Male	40	57.76	No	No	14.02	196.61
Female	30	57.87	No	No	14.13	199.66
Male	33	58.05	No	Yes	14.31	204.90
Male	38	58.45	Yes	Yes	14.71	216.51
Female	36	61.37	Yes	No	17.63	310.76
Male	53	62.30	No	No	18.56	344.54
Male	56	64.47	No	Yes	20.74	429.96
Male	48	64.48	No	Yes	20.74	430.22
Male	54	64.70	Yes	No	20.96	439.40
Female	49	64.73	Yes	No	20.99	440.45
Male	55	67.65	Yes	Yes	23.92	571.99
Male	60	78.91	Yes	No	35.18	1237.36
Female	43	82.89	Yes	Yes	39.16	1533.24
Male	56	98.98	Yes	Yes	55.24	3051.11
		3761.48				18477.35

Sum of all Wages	3761.48
Count of Employees	86
Mean Wage	43.74
Median Wage	41.30
Mode	50
(X-)^2 / n-1	217.38
Standard Deviation	14.74

Column1
Mean	43.73814837
Standard Error	1.58986838
Median	41.29583
Mode	50
Standard Deviation	14.74383282
Sample Variance	217.3806062
Kurtosis	1.460297716
Skewness	0.893772364
Range	78.38125
Minimum	20.59375
Maximum	98.975
Sum	3761.48076
Count	86
	0