The diameter of 3.5 centimetre discs is normally distributed.Periodically, quality control inspectors at Winnipeg Discs randomly select a sample of 16 discs.If the mean diameter of the discs is too large or too small the disc punch is shut down for adjustment; otherwise, the punching process continues.The last sample showed a mean and standard deviation of 3.55 and 0.08 centimetres, respectively.Using $\alpha$= 0.05, the appropriate decision is ___.
A)reject the null hypothesis and shut down the punch
B)reject the null hypothesis and do not shut down the punch
C)do not reject the null hypothesis and shut down the punch
D)do not reject the null hypothesis and do not shut down the punch
E)do nothing

Question

Quizplus · Accepted Answer

The null hypothesis is that the mean diameter is 3.5 cm. With a sample mean of 3.55 cm, a standard deviation of 0.08 cm, and a sample size of 16, the test statistic is calculated. The critical value for a two-tailed test at $\alpha$ = 0.05 is approximately ±2.131. If the test statistic exceeds this critical value, the null hypothesis is rejected, indicating the punch should be shut down for adjustment.

The Diameter of 3 α\alphaα = 005, the Appropriate Decision Is ___

The Diameter of 3 $\alpha$ = 005, the Appropriate Decision Is ___