Suppose we have measurements under experimental conditions on the loss of volume
ID: 1868121 • Letter: S
Question
Suppose we have measurements under experimental conditions on the loss of volume due to wear of 32 specimens under a water-based lubricant, and another separate 32 specimens under an oil-based lubricant. So there were a total of 64 specimens, which were randomly allocated to either the water-based or the oil-based treatment group The wear loss (in mL) under the water-based lubricant is as follows: 60, 37, 49,57,51, 34, 49, 50, 47, 41, 41, 41, 41, 54, 32, 36, 49, 30, 43, 40, 32, 44, 50, 38, 30, 60, 50, 36, 45, 56,50, 38] The wear loss (in mL) under the oil-based lubricant is as follows: 60, 54, 46, 59, 55, 63, 41, 65, 46, 46, 43, 59, 53, 51,39, 39, 56, 38,36, 48, 56, 38, 38, 51, 37, 58, 55,61, 45, 38, 44, 38 Use Matlab to test for evidence that lubricant affects wear loss, at the 0.01 significance level, assuming equal variances. That is, test for evidence that average wear loss differs between the water-based and oil-based treatments. Find a P-value for this test (to 3 decimal places) Number Which of the following best summarises what you can conclude from this test? O There is evidence that lubricant does not affect mean wear loss There is evidence that lubricant affects mean wear loss. There is no evidence that lubricant affects mean wear loss.Explanation / Answer
First let us input the given 64 specimens values into 2 vectors in Matlab:
>> x = [60,37,49,57,51,34,49,50,47,41,41,41,41,54,32,36,49,30,43,40,32,44,50,38,30,60,50,36,45,56,50,38]
>> y = [60,54,46,59,55,63,41,65,46,46,43,59,53,51,39,39,56,38,36,48,56,38,38,51,37,58,55,61,45,38,44,38]
Now here our Null Hypothesis is that, There is an evidence that lubricant affects the wear loss.
Let us test this hypothesis with 0.01 significance level using following code in Matlab:
>> [h,p] = ttest(x,y,'Alpha',0.01)
We get following output:
h =
0
p =
0.0232
Since h = 0, Null hypothesis is not rejected.
This indicates that There is evidence that Lubricant affects mean wear Loss with P value = 0.0232