Question

15. Manufactured Machine Parts A manufacturing process produces machine parts with measurements the standard deviation of which must be no more than 0.52 mm. A random sample of 20 parts in a given lot revealed a standard deviation in measurement of 0.568 mm. Is there sufficient evidence at a = 0.05 to conclude that the standard deviation of the parts is out- side the required guidelines?

Answer 1

Given:

$1587156385764_blob.png$ = 0.05, n = 20, S = 0.568, $1587156385804_blob.png$ = 0.52

Hypothesis:

Ho: $1587156385810_blob.png$ = 0.52

Ha: $1587156385822_blob.png$ < 0.52

Test statistic:

12_(n-1) (20 – 10.568 -= 22.67 0.522

P-value: 0.2522           ..........................Using Chi square table

Conclusion:

P-value > $\alpha$ , i.e. 0.2522 > 0.05, That is Fail to Reject Ho at 5% level of significance.