Question

A machine is adjusted so that the mean of a certain component of parts used in the aircraft navigation system is 21cm. A random sample of 12 of these components of the parts revealed a mean of 21.7cm and a standard deviation of 0.3cm? Do these results indicate that the machine is out of adjustment? Test at the 0.05 level of significance.

Answer 1

We know that:

Population mean, mu= 21cm

Sample mean, xbar= 21.7cm

Sample standard deviation, s= 0.3cm

Sample size, n= 12

Null hypothesis: H0: mu= 21cm

Alternate hypothesis: Ha: mu not equal to 21cm.

Thus, we know that this is a two tailed test.

Thus, the critical value of t at 0.05 at 11 degree of freedom is 2.200985.

The t statistic= (xbar-mu)/s/sqrt(n)

= (21.7-21)/0.3/sqrt(11)

= 7.738791

Since this is beyond the critical value, we reject the null hypothesis and conclude that the machine is out of adjustment, at 95% confidence level.