The following shows the number of shirts by sizes that are manufactured in a factory on a particular week:   Extra Small = 390 Small = 470 Medium = 520   Large = 628 Extra Large = 440 It was discovered that the sizing of some shirts was labelled incorrectly. (i) Give two reasons why it would be necessary to examine a sample of the shirts produced rather than examine the entire weekly production. (ii) State two differences between a cluster sample and a stratified random sample in this situation. (iii) Using the stratified random sampling technique, calculate the number of medium shirts that will be selected if we require a sample of 375 shirts. (iv)State one advantage of using the stratified random method for collecting this sample.

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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.