Question

Once calculations and interpretations are complete upload excel file into submission area

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The US government stated that it pays fire fighters at least $100,000 annually. Fire Fighters Labor Union believes that the amount the US government says it pays firefighters in salary is less than the stated amount of at least $100,000 and takes a sample of some of its employees in California (see excel data for the information). Is there enough evidence to support the Fire fighters labor union claim at alpha = 0.05?

Employee Identifier	Job	Salaries	Total Compensation
4053	Firefighter	77396.3	133592.49
39839	Firefighter	117156.2	185958.11
26574	Firefighter	119258.6	189229.8
35177	Firefighter	118184.8	187802.36
5580	Firefighter	47016	65481.63
42143	Firefighter	114949.7	177530.84
20724	Firefighter	119258.7	186970.1
18961	Firefighter	107397.5	189528.48
14624	Firefighter	119258.6	180591.24
14942	Firefighter	82924.41	144450.39
25402	Firefighter	69330.7	107689.58
41240	Firefighter	111361.4	194832.48
23234	Firefighter	119280.1	212597.94
36619	Firefighter	70026.57	110697.99
2804	Firefighter	84419.58	154247.3
16789	Firefighter	81140.89	148647.84
32882	Firefighter	118184.8	248991.92
15689	Firefighter	7200	10322.97
50173	Firefighter	76579.08	125149.55
19410	Firefighter	7200	10296.55
40211	Firefighter	118184.8	285810.79
13419	Firefighter	113763.2	226451.75
12106	Firefighter	131679.1	183309.22
26514	Firefighter	107448.4	169818.23
42022	Firefighter	133269.2	200024.41
2050	Firefighter	47016	74768.59
18686	Firefighter	116598.2	165975.87
9143	Firefighter	119258.6	192822.87
611	Firefighter	113726.1	224645.5
51954	Firefighter	119258.6	264029.62
40295	Firefighter	81299.34	158004.45
31475	Firefighter	119258.6	217534.66
4551	Firefighter	60135.04	156507.74
5903	Firefighter	119258.6	210723.11
48745	Firefighter	70040.36	111713.39
32854	Firefighter	119258.6	194684.51
21364	Firefighter	77310.41	132180.54
30422	Firefighter	77310.42	132044.92
8988	Firefighter	118184.8	244423.16
1706	Firefighter	119258.6	261158.15
1756	Firefighter	83582.07	129582.07
24742	Firefighter	83363.25	142048.34
33211	Firefighter	113726.1	198709.86
18031	Firefighter	90791.95	144224.18
54880	Firefighter	113824	212346.12
35242	Firefighter	77274.92	136059.41
30841	Firefighter	119258.7	240355.55
43324	Firefighter	118184.8	222776.53

Answer 1

μ = 100000

x (Using Excel function AVERAGE( )) = AVERAGE(salaries) = 96855.14

s (Using Excel function STDEV.S( )) = STDEV.S(salaries) = 29463.35

n = 48, Degrees of freedom: df = n-1 = 47

Level of significance = 0.05

H₀: μ > 0, US government pays fire fighters at least 100,000 annually

H₁: μ < 100000, US government pays fire fighters less 100,000 annually

Test statistic = (x-μ)/(s/n^0.5) = (96855.14-100000)/(29463.35/48^0.5) = -0.74

p-value (Using Excel function T.DIST(test statistic, df, cumulative)) = T.DIST(-0.74,47,TRUE) = 0.231

Since p-value is more than 0.05, we do not reject the null hypothesis.

So, US government pays fire fighters at least 100,000 annually. There is not enough evidence to support the Fire fighters labour union claim.