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 3.49 and 0.08 centimetres, respectively.Using $\alpha$ = 0.05, the critical "t" values are ___.
A)-2.120 and 2.120
B)-2.131 and 2.131
C)-1.753 and 1.753
D)-1.746 and 1.746
E)-2.567 and 2.567

Question

Quizplus · Accepted Answer

Since we are using a t-test with a sample size of 16 and a significance level of 0.05, we need to find the critical t-values using a t-distribution table with 15 degrees of freedom (df= n-1). The critical values are obtained by finding the values that accumulate to 0.025 in the lower tail and 0.025 in the upper tail of the t-distribution table. The closest values to 0.025 in the table are 2.131 and -2.131, which correspond to a two-tailed test. Therefore, the critical t-values are -2.131 and 2.131. Thus, the correct choice is B.

The Diameter of 3 α\alphaα = 005, the Critical "T" Values Are ___

The Diameter of 3 $\alpha$ = 005, the Critical "T" Values Are ___