Discussion: Applications of Hypothesis Tests

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Hypothesis testing is very applicable in the daily life and typically occurs at the instances when either certainty or uncertainty of an average is to be confirmed. My application comes in determining the average number of cups coffee that the customers at my friends’ coffee shop take every evening. The number often varies depending on the weather condition of the evening, normally when it is too cold, more cups are likely to be sold and on the contrary on a normal day the sales do not shoot up.
The average cups of coffee sold at the shop is 100 cups. This is a two-tailed hypothesis because by using the term “is” it means that the term should be equal to the number. On a typical evening, the shop sales averages at 100 cups and this may be less on a day when the sales are not very good, however on days when the weather is so cold the number of cups sold may increase. Therefore, our null hypothesis will be equal to 100 and the alternate hypothesis in not equal to 100 because it may be less or more.
Null Hypothesis: H0: μ=100Alternate hypothesis : Ha: μ≠100The test may lead to the type I error when we can accept that the average number of cups of coffee sold at the shop is 100 when in reality this may not be true. On the other hand, we may conclude that the average number cups sold at the shop is 100 when in the real sense the number is more which is the type II error.
The two-tailed test is important in testing for the validity of a mean when the outcome may lie either at the upper or lower side of the proposed mean.