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The Production Department

The Production Department is not convinced with the supplier’s claim that their sack of potatoes (a snack food ingredient) weighs 50 kilograms each. There were instances when, upon checking, a sack would only weigh 47 kilos. Since the process of finding another trustworthy supplier can be time-consuming and costly, the Production Supervisor could only plan on gathering enough evidence to contest the supplier’s claim.

The Production Supervisor then asked his assistant to pick up 10 random samples from each of the succeeding three deliveries over a two-week period. Upon weighing, a sample mean weight of 50.5 kgs. and a standard deviation of 2.3 kgs. were noted for the 30 potato sack samples.

Easton and McColl (1997) define a null hypothesis as a theory that is forwarded, because of the belief that it is true or because of its possible use as an argument basis, but is still awaiting proof. In contrast, Easton and McColl (1997) define an alternative hypothesis as a statement that a hypothesis test will confirm. The null hypothesis in the potato weight issue is that the potato sacks have a population mean weight of 50 kgs. (HO: µ = 50 kgs.). The alternative hypothesis, however, is that the potato sacks have a population mean weight less than 50 kgs. (HA: µ < 50 kgs.). While there is nothing wrong with accepting a true null hypothesis and rejecting a false one, an error is committed by rejecting a true null hypothesis and accepting a false one.

Freund, Williams, and Perles (1997) define a type I error as the error committed by rejecting a true null hypothesis; if the null hypothesis is true and it gets rejected, a type I error is committed. In this case, a type I error is committed if the potato sacks indeed have a population mean weight of 50 kgs. and this null hypothesis is rejected. WidgeCorp then will have to needlessly confront its supplier about this issue or plan on sourcing potatoes from other suppliers. The company will have to exert effort and incur extra costs in contacting potential potato suppliers.

A lawsuit might also be imminent in case a termination of a contract with the supplier becomes necessary. The company will incur litigation costs in this scenario. Freund et al., (1997), however, define a type II error as the error committed by accepting a false null hypothesis; if the null hypothesis is false and it gets accepted, a type II error is committed. In this case, a type II error is committed if the supplied potato sacks have a population mean weight less than 50 kgs. and the null hypothesis is accepted. Naturally, WidgeCorp will stick to its original supplier, be made to pay a higher per kilo price for its potatoes and lose possible profits from this arrangement. Committing any of the two types of error can have serious implications for a business in the long run and should thus be avoided.

References

Easton, V. J., & McColl, J. H. (Sept. 1997). Statistics Glossary. Retrieved March 11,       2009, from http://www.stats.gla.ac.uk/steps/glossary/hypothesis_testing.html#h0 

Freund, J. E., Williams, F. J., & Perles, B. M. (1997). Elementary business statistics: The modern approach (6th ed.). Singapore: Simon & Schuster Pte. Ltd. 

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