Question

The last time that information on employees working at this bank was collected, the number of months of previous work experience was distributed such that 15% of employees had a less than 2 years of experience, 25% had between 2 and 5 years of experience, 20% had more than 5 years and up to 10 years of previous work experience, and 40% had more than 10 years of experience. Verify at a 0.05 level of significance if the current data presents the same distribution. What is your conclusion?

Current data (n=93): Number of years of experience

0,44,5,6,8,0,0,5,75,52,8,52,70,6,11,11,63,144,163,228,381,214,318,96,36,59,115,165,123,18,102,127,90,190,107,173,228,26,36,38,82,169,244,24,49,51,122,97,196,133,55,90,117,51,61,241,121,79,209,87,231,12,14,180,315,29,7,38,113,18,359,36,320,24,32,49,56,252,272,25,36,56,64,108,46,72,64,84,216,42,175,132,55

Answer 1

Category	Observed Frequency (O)	Proportion, p	Expected Frequency (E)	(O-E)²/E
Less than 2 years(i	16	0.15	93 * 0.15 = 13.95	(16 - 13.95)²/13.95 = 0.3013
2 - 5 years	26	0.25	93 * 0.25 = 23.25	(26 - 23.25)²/23.25 = 0.3253
5 - 10 years	21	0.2	93 * 0.2 = 18.6	(21 - 18.6)²/18.6 = 0.3097
More than 10 years	30	0.4	93 * 0.4 = 37.2	(30 - 37.2)²/37.2 = 1.3935
Total	93	1.00	93	2.3297

Null and Alternative hypothesis:  
Ho: Proportions are same.  
H1: Proportions are different.  
Test statistic:  
χ² = ∑ ((O-E)²/E) = 2.3297
df = n-1 = 3
Critical value:  
χ²α = CHISQ.INV.RT(0.05, 3) = 7.8147  
p-value:  
p-value = CHISQ.DIST.RT(2.3297, 3) = 0.5068  
Decision:  
p-value > α, Do not reject the null hypothesis  
There is not enough evidence to reject the claim that the current data presents the same distribution at 0.05 significance level.