Show all work. Use Minitab as much as you can and show graphs. (Montgomery & Run
ID: 3376470 • Letter: S
Question
Show all work. Use Minitab as much as you can and show graphs. (Montgomery & Runger, 2007; ) Question : The titanium content in an aircraft-grade alloy is an important determinant of strength. A sample of 20 test coupons reveals the following titanium content (in percent): 8.32, 8.05, 8.93, 8.65, 8.25, 8.46, 8.52, 8.35, 8.36, 8.41, 8.42, 8.30, 8.71, 8.75, 8.60, 8.83, 8.50, 8.38, 8.29, 8.46 The median titanium content should be 8.5%. (a) Use the Sign Test with confidence interval level of 95% to investigate this hypothesis. (b) Use the Sign Test to test the median of 8.5%. What is the p-value for this test?
Explanation / Answer
Result:
Show all work. Use Minitab as much as you can and show graphs. (Montgomery & Runger, 2007; ) Question : The titanium content in an aircraft-grade alloy is an important determinant of strength. A sample of 20 test coupons reveals the following titanium content (in percent): 8.32, 8.05, 8.93, 8.65, 8.25, 8.46, 8.52, 8.35, 8.36, 8.41, 8.42, 8.30, 8.71, 8.75, 8.60, 8.83, 8.50, 8.38, 8.29, 8.46 The median titanium content should be 8.5%.
MINITAB used.
Sign CI: titanium content
Method
?: median of titanium content
Descriptive Statistics
Sample
N
Median
titanium content
20
8.44
95% Confidence Interval for ?
Sample
CI for ?
Achieved
Confidence
Position
titanium content
(8.36, 8.52)
88.47%
(7, 14)
(8.35235, 8.58118)
95.00%
Interpolation
(8.35, 8.6)
95.86%
(6, 15)
The value 8.5 falls in the interval (8.35, 8.58) , Ho is not rejected.
We conclude that titanium content should be 8.5%.
(b) Use the Sign Test to test the median of 8.5%. What is the p-value for this test?
Sign Test for Median: titanium content
Method
?: median of titanium content
Descriptive Statistics
Sample
N
Median
titanium content
20
8.44
Test
Null hypothesis
H?: ? = 8.5
Alternative hypothesis
H?: ? ? 8.5
Sample
Number < 8.5
Number = 8.5
Number > 8.5
P-Value
titanium content
12
1
7
0.359
P value = 0.359
?: median of titanium content