In any hypothesis testing we have to decide on the level of significance which is denoted by alpha. This is important as failure to choose correctly null hypothesis can cause Type 1 error.
IF α is small - There is lass chance of incorrectly rejecting a Null hypothesis (H0)
Since the power is low this decreases the chance of detecting an effect if one exists
IF α is Large - There is a higher chance of incorrectly rejecting the Null hypothesis (H0)
Since the power is high there is high chance of detecting the effect
To Select α for a Hypothesis test we need to understand which mistake will be worse ,finding an effect which does not really exist or not finding an effect that does exists .
Examples where α is Small-
1. Buying an expensive machine as the cost might be very high and we might set a very low α so that we are able to determine if there is any effect on productivity post buying the new machine
2. Fitting a new car model with a new engine Vs a old one
3. Changing the breaking system in an elevator with a new mechanism which is more economical. This can have serious impact on safety if the machine fails to work
4. Changing a bearing in a jet plane with new ones which are less expensive
5. Using cheaper building material for construction to bring down overall cost of the project. In order to save money if the company replaces the material there can be serious implication to the lives of people
6. New Iron & steel used in a dam construction project from a different vendor who is offering a discount
7. New material used for GAS pipeline Vs the old one which can reduce the cost. If the company does not test this adequately then there can be major catastrophe and company can be answerable to government & public
Examples where α is Large-
1. Checking the effectiveness of a new delivery model for a chain of restaurant which is already getting customer complaints due to delivery delays
2.A new Sales strategy for a firm which is making losses due to low sales
3. A decision for Digital strategy implementation for a company which is on verge of bankruptcy
4.A new repair allocation process for a Insurance company which is loosing customer base due to the high claims life cycle time
The above are some examples which will help to decide whether to take a higher or lower α value.