Question

uL 10IAê workers are paid on average less than (a) (2 points) State the Null and Alternative hypotheses. (b) (3 points) Calculate the test statistic. (c) (3 points) Calculate (or estimate) the p-value for the test. (d) (3 points) State and interpret your conclusion. 12. Historically, a bank has employed 50% permanent full-time workers, 25% permanent part-time workers, 15% temporary full-time workers, and 10% temporary part-time workers. In a recent sample of 400 workers, 190 were permanent full-time, 125 were permanent part-time, 55 were temporary full-time, and 30 were temporary part-time. Use these data and a = 0.05 to assess whether there has been a change from the historical percentages. Category permanent full-time Percent Observed 50% 190 permanent part-time temporary full-time temporary part-time 25% 125 15% 10% 55 30 (a) (2 points) State the Null and Alternative hypotheses. (b) (3 points) Calculate the test statistic. (c) (3 points) Calculate (or estimate) the p-value for the test. (d) (3 points) State and interpret your conclusion.

Answer 1

a)

Ho: there is no change from historical percentage
Ha: there is a change from historical percentage

b)

observed frequencey, O	expected proportion	expected frequency,E	(O-E)	(O-E)²	(O-E)²/E
190	0.5000	200.000	-10.00	100.00	0.500
125	0.2500	100.000	25.00	625.00	6.250
55	0.1500	60.000	-5.00	25.00	0.417
30	0.1000	40.000	-10.00	100.00	2.500

chi square test statistic,X² = Σ(O-E)²/E =   9.6667

c)

Degree of freedom=k-1=   4   -   1   =   3
                  
P value =   0.0216   [ excel function: =chisq.dist.rt(test-stat,df) ]          

d) Decision: P value < α, Reject Ho

there is enough evidence to conclude that there is a change from historical percentage