Question

Machine A and machine B produce identical components and it is required to test if the mean diameter of the components is the same. A random sample of 144 from machine A had a mean of 36.4 mm and a standard deviation of 3.6 mm; whilst a random sample of 225 from machine B had a mean of 36.90 mm and a standard deviation of 2.9 mm.
Are the means significantly different at the 5% level?

Answer 1

Solution

$H_0: \mu_1- \mu_2=0$ vs

$H_1: \mu_1-\mu_2 \not= 0$

Test statistic :

$$Z-test= {(\bar{x}_1 - \bar{x} _2)-(\mu_1 - \mu_2) \over \sqrt {{S_1^2\over n_1}+{S_2^2 \over n_2}} }$$

$$={(36.4-36.90)-0 \over {\sqrt{{3.6^2 \over 144}+{2.9^2 \over 225}}} }$$

$$=-1.400$$

Z-value:

$Z_{0.025}=1.96 \space and \space - 1.96$

Since the test statistic lies between -1.96 and 1.96, we fail to reject the null hypothesis.

Therefore there is no sufficient evidence to support the claim that the machine A is significantly different from machine B.