Hypothesis testing for single mean.
Assume that the measurements came from a normal distribution. The variability of the manufacturing process is unknown means the same as the standard deviation is unknown.
Auto crank shafts. Here are measurements (in millimeters) of a critical dimension for 16 auto engine crankshafts:
|
224.120
|
224.001
|
224.017
|
223.982
|
223.989
|
223.961
|
|
223.960
|
224.089
|
223.987
|
223.976
|
223.902
|
223.980
|
|
224.098
|
224.057
|
223.913
|
223.999
|
|
|
The dimension is supposed to be 224 mm and the variability of the manufacturing process is unknown. Is there evidence that the mean dimension is not 224mm?
1. The appropriate test to use is
a. TTest b. 1-PropZtest c. ZTest d. Paired T test
2. The appropriate type of test to use based on the tails of the distribution
a. Left-tailed b. Two-tailed c. Right-tailed
3. The p-value of the test is closest to
a. 0.9289 b. 0.0431 c. 0.0134 d. 0.9019
4. Based on the above analysis (p-value and α= 0.025), we conclude that
a. The mean dimension of crankshafts is 224mm.
b. The mean dimension of crankshafts is 224mm.
c. We do not have sufficient information to draw a conclusion