A tire manufacturing company invents a new cheaper method fo

A tire manufacturing company invents a new, cheaper method for carrying out one of the steps in the manufacturing process. The company wants to test the new method before adopting it, because the method could alter the interply shear strength of the tires produced. To test the acceptability of the new method, the company formulates the null and alternative hypotheses as

Where µ1 is the population mean of the interply shear strength of the tires produced by the old method and µ2 that of the tires produced by the new method. The evidence is gathered through a destructive test of 40 randomly selected tires from each method. Following are the data gathered:

The manufacturer moves to reduce the variance of the strength by improving the process. Will the reduction in the variance of the process increase or decrease the chances of type I and type II errors?

Solution

Since Power is the probability of correctly rejecting a false null hypothesis, It is to our best interest to increase power

Ways of increasing Power

• make alpha larger

• use one-tailed rather than two tailed test

• decrease variance – increase sample size – better measures

• increase effect size

Thus decresae in variance decreses the type II error.

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For type I error we find the p value from the difference between x and hypothesised x divided by std error

Std error if increases then test statistic decreases and vice versa

Hence decrease in std error reduces the type I error also