minimum sample size proportion: quality control check


Case Study:
An automotive tire manufacturer wishes to estimate the difference in mean wear of tires manufactured with an experimental material and ordinary production tire, with 90% confidence and to within 0.5 mm. To eliminate extraneous factors arising from different driving conditions the tires will be tested in pairs on the same vehicles. It is known from prior studies that the standard deviations of the differences of wear of tires constructed with the two kinds of materials is 1.75 mm. Estimate the minimum number of pairs in the sample necessary to meet these criteria.

Solution: 
#Input:
 Error = .5
 alfa = 0.9
 std_d = 1.75
 
#estimating min sample size: 
 
z_value = qnorm((1-alfa)/2, 
       mean = 0, 
       sd = 1)
 
sample_size = ceiling((z_value^2 *std_d^2)/Error*2
)

Conclusion:
The minimum sample size required is 34 units

   

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