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?

Answer 1

(a)

Enter the data in a column, say C1

go to stat -> nonparametrics -> 1-Sample Sign test

in variables , enter C1

select confidence interval

set level equal to 95%

press OK

The result is given below:

The interpretation isas follows:

Minitab calculates three intervals. The first and third intervals have confidence levels below and above the requested level, respectively. The confidence levels are calculated according to binomial probabilities. The interval that goes from the 6th smallest observation to the 6th largest observation has a confidence of 0.9586, and the interval that goes from the 7th smallest observation to the 7th largest observation has a confidence of 0.8847. The middle interval is found by a linear interpolation , which has the desired confidenced level.

Means, their is 0.95 probability that the population median will lie between 8.325 and 8.581.

sample median is 8.44

(b)

Enter the data in a column, say C1

go to stat -> nonparametrics -> 1-Sample Sign test

in variables, enter C1

select test median

enter 8.50 in the text box

choose alternate : not equal

press OK

the result i given below:

Clearly, p-value is > 0.05

(p-value=0.3593)

Conclusion is: based on this sample we fail to reject the null hypothesis that median is 8.5