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

We have to test that current data represents the same distribution. We use chi-square test for goodness of fit to test that current data represents the same distribution.

Here, we test -

H₀ : the current data have come from the same distribution.

H₁ : the current data have not come from the same distribution.

Test statistic -

Test criterion -

We reject H₀ if   _,n-p-k-1

Where, n is number of classes, k is number of pullings, p is number of parametres estimated.

Observation table -

Experience	frequency(Oi)	Probability(Pi)	Ei = N*Pi	di = (Oi - Ei)^2	di/Ei
less than 2	18	0.15	13.95	16.4025	1.1758
2-5	24	0.25	23.25	0.5625	0.0242
5-10	21	0.2	18.6	5.76	0.3097
more than 10	30	0.4	37.2	51.84	1.3935
Total	93	1	93		2.9032

Calculations -

Critical value -

_,n-p-k-1 =  _0.05,4-0-0-1 =  _0.05,3 = 7.81

n is number of classes = 4, k is number of pullings = 0, p is number of parametres estimated = 0

Conclusion -

Here, (2.9032) < _,n-p-k-1  (7.81) ,hence We accept H₀ at 5% level of significance.

i.e. There is clear evidence that current data represents the same distribution.

Note : Chi-square table is provided below.