Question

• A new diagnostic technique (A) is tested on the line to determine if instrumentation is flawed.
• It is being compared to the older method (B) with respect to minutes before a correct conclusion is reached.
• Although the sample may look normal it is known that the underlying population is NOT normal.
• Is method A superior to B?
  • Test at an alpha = 0.05

A	B
5	8
4	10
3	11
5	2
5	6
4	9
9	6
6	9
7	12
6	13

Answer 1

Suppose, random variables X and Y denote time taken to reach correct conclusion for methods A and B respectively.

Here, two different groups are used to collect data in two different methods. Further we do not know population standard deviation (or variance). Though population does not follow Normal distribution, sample seems to follow approximately Normal distribution. So, we have to perform two sample t-test.

A diagnostic technique is better if it takes less time to reach correct conclusion.

We have to test for null hypothesis

against the alternative hypothesis

Our test statistic is given by

Here,

First sample size

Second sample size

Sample mean of first sample is given by

Sample mean of second sample is given by

Pooled sample variance is given by

Degrees of freedom

[Using R-code 'pt(-2.739505,18)']

Level of significance

We reject our null hypothesis if

Here, we observe that

So, we reject our null hypothesis.

Hence, based on the given data we can conclude that there is significant evidence that method A is superior to B.