Question

2. The following table presents the numbers of emplovees, by age group, who were promoted, or not promoted, in a sample drawn from a certain industry during the past ycar. Age 40-49 50 and Over 3039 Under 30 8 29 24 19 Promoted 42 47 49 34 Not Promoted Can you conclude that the people in some age groups are more likely to be promoted than those in other age groups? Use the a 0.01 level of significance. (a) State the null and alternative hypothesis (b) State the significance level (c) Compute the appropriate statistic (d) Find the critical value(s) and draw the rejection region (e) Interpret the results

Answer 1

Hypothesis :

H0 : p1 = p2 = p3 = p4

Ha : at least one proportion is different

Observed
	Age
Row variable	Under 30	30-39	40-49	50 and Over	Total
Promoted	19	29	24	8	80
Not Promoted	34	47	49	42	172
Total	53	76	73	50	252
Expected
	Under 30	30-39	40-49	50 and Over		Row Totals
Promoted	19  (16.83)  [0.28]	29  (24.13)  [0.98]	24  (23.17)  [0.03]	8  (15.87)  [3.91]		80
Not Promoted	34  (36.17)  [0.13]	47  (51.87)  [0.46]	49  (49.83)  [0.01]	42  (34.13)  [1.82]		172
Column Totals	53	76	73	50		252  (Grand Total)

df = (c-1) * (r-1) = (2-1) * (4-1) = 3

The chi-square statistic is 7.6182.

Critical value = 11.345.

The p-value is .054599.

The result is not significant at p < .01.

We do not reject H0

So we conclude that there is not enough evidence to conclude that promotion is independent of age