Question

The margin of error for a multiple comparisons procedure was determined to be 10.5 units. The sample means for the problem were: A: 47.3 B: 22.5 C: 19.5 D: 38.6. Which of the following statements is INCORRECT?

There IS a significant difference between groups A and B

There IS a significant difference between groups A and C

There is NO significant differences between groups A and D

There is NO significant differences between groups B and C

There is NO significant differences between groups B and D

Answer 1

Solution:

Given:

E = Margin of Error = 10.5

The sample means for the problem were: A: 47.3 B: 22.5 C: 19.5 D: 38.6.

We have to identify incorrect statement from given statements.

Lets consider first one:

There IS a significant difference between groups A and B

For group A , mean = 47.3 and for group B , mean = 22.5

Thus lower and upper limits of confidence interval are:

If confidence interval includes 0, then we say there is no significant difference and if it does not include 0 , that is both the limits are either negative or positive, then we say there is significant difference between two means.

Since confidence interval for group A and B is : which does not include 0, hence there is significant difference between means of group A and B.

Thus first statement is Correct.

Now consider second statement:

There IS a significant difference between groups A and C

Find confidence interval:

For group A , mean = 47.3 and for group C , mean = 19.5

Thus lower and upper limits of confidence interval are:

Since confidence interval for group A and C is : which does not include 0, hence there is significant difference between means of group A and C.

Thus second statement is Correct.

Now consider third statement:

There is NO significant differences between groups A and D

For group A , mean = 47.3 and for group D , mean = 38.6

Thus lower and upper limits of confidence interval are:

Since confidence interval for group A and D is :   which includes 0, hence there is NO significant difference between means of group A and D.

Thus third statement is Correct.

Now consider fourth statement:

There is NO significant differences between groups B and C

For group B , mean = 22.5 and for group C , mean = 19.5

Thus lower and upper limits of confidence interval are:

Since confidence interval for group B and C is :   which includes 0, hence there is NO significant difference between means of group B and C.

Thus fourth statement is Correct.

Now consider fifth statement:

There is NO significant differences between groups B and D

For group B , mean = 22.5 and for group D , mean = 38.6

Thus lower and upper limits of confidence interval are:

Since confidence interval for group B and D is :   which does not include 0, hence there is significant difference between means of group B and D.

But statement is: There is NO significant differences between groups B and D

Thus this is incorrect statement.

Thus correct option is fifth option for incorrect statement.