A clothes distributor is supposed to deliver a large quantity of coats to a foreign consignment in England. The dealer has ordered 47% to be white, 33% black, 20% green. A random sample of 300 coats was selected by an inspector and 150 white, 85 black and 65green coats were counted. We want to test the hypothesis whether the delivery of sweaters follows the claimed probabilities'?
In this problem we want to run a test of goodness of fit to check whether the coats in the consignment follow the indicated probabilities. This is a non-parametric test and ANOVA cannot be applied because it does not satisfy the assumption of equality variances, or even an underlying normal distribution.
HO: The delivery of coats follows the claimed probabilities'
HA: The delivery of coats does not follow the claimed probabilities.
The level of significance: a =5%
The decision rule: Reject the null hypothesis if p-value < 0.05
Calculations:
Observed (0) White= 150; black =85; green = 65; Sum = 300
Expected (E) White =141; Black = 99; Green = 60; Sum =300
0- E White =9. 00; Black = 14.00; Green= 5.000; Sum = 0.000
% of x 2 White = 19. 34; Black = 66. 64; Green = 14.02; Sum = 100.00
2.97 x2
2 dof
.2264 p-values
Conclusion: Since the p-value is not less than 0.05, I do not reject the null hypothesis. Therefore, there is insufficient evidence to conclude at 5% level of significance that the delivery does not come in the probabilities as claimed by the distributor.
Effect size for symbol small medium large Chi-Square Test w 0. 10 0.30 0.50