Lena will use boards similar to the one shown below to build shelves

a) If we design the experiment on this way we can check if we have an improvement with the method used.

We assume that we have the same individual and we take a value before with the normal impaired condition and the final condition is the normal case.  

b)  

The 95% confidence interval would be given by (-1.24;-0.69)

Step-by-step explanation:

Part a

If we design the experiment on this way we can check if we have an improvement with the method used.

We assume that we have the same individual and we take a value before with the normal impaired condition and the final condition is the normal case.

Part b

For this case first we need to find the differences like this :

Normal, Xi 4.47 4.24 4.58 4.65 4.31 4.80 4.55 5.00 4.79

Impaired, Yi 5.77 5.67 5.51 5.32 5.83 5.49 5.23 5.61 5.6

Let

The second step is calculate the mean difference  

The third step would be calculate the standard deviation for the differences, and we got:

The confidence interval for the mean is given by the following formula:  

(1)  

In order to calculate the critical value we need to find first the degrees of freedom, given by:  

Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,8)".And we see that  

Now we have everything in order to replace into formula (1):  

So on this case the 95% confidence interval would be given by (-1.24;-0.69)