Question

An automobile parts supplier manufactures a cylindrical engine part. The part is supposed to have an outside diameter of four centimetres. Parts with diameters that are too large or too small will not fit properly within the engine and must be discarded, resulting in a loss of time and materials. The quality control department routinely inspects the manufacturing process to determine if the parts are meeting the specification. The most recent random sample of 36 parts produced a sample mean of 4.005 cm. Assume that the population standard deviation of the diameter is known to be 0.014 cm. Is there sufficient evidence to suggest that the parts are not meeting the target diameter? Use the p-value method to conduct an appropriate hypothesis test at the 5% level of significance. Comment on the validity of your conclusion.

Answer 1

H0; Null Hypothesis: = 4

HA: Alternative Hypothesis: 4

SE = /

= 0.014/

= 0.002333

Test Statistic is given by:
Z = (4.005 - 4)/0.002333

= 2.1429

Table of Area Under Standard Normal Curve gives area = 0.4838

So,

p - value = (0.5 - 0.4838) X 2

= 0.0324

Since p - value = 0.0324 is less than = 0.05, the difference is significant. Reject null hypothesis.

Conclusion:

There is sufficient evidence to suggest that the parts are not meeting the target diameter.

The conclusion is valid because the population SD is provided and the Sample Size = n = 36 > 30 Large Sample and Central Limit Theorem is applicable. So, Z score is applied.