Question

The manufacturer of a widely used hand lotion wishes to compute the effectiveness of its product, Lotion A, with another leading product, Lotion B. The manufacturer elicits the help of 50 women living in Minneapolis, Minnesota (where dry skin is a real problem in the winter). These women are then randomly assigned to two groups. Group 1 receives Lotion A and group 2 receives Lotion B. Each woman then reports the number of days she found it necessary to use her hand lotion before noticing signs of improvement. Their responses are listed below. Complete a test of the null hypothesis of no difference between lotions using an alpha level of .05. Be sure to complete all necessary steps.

Group 1 (Lotion A)

2,3,4,3,2,3,1,2,3,2,4,3,3,3,4,3,2,4,3,2,3,4,3,1,2

Group 2 (Lotion B)

4,3,3,2,4,5,3,4,3,3,2,2,4,3,3,2,5,3,4,3,3,2,3,4,4

Answer 1

We will use Ai for Group 1 that receives Lotion A and Bi for group 2 which receives Lotion B.

Now I think there is a typing error in

Group 1 (Lotion A)

2,3,4,3,2,3,1,2,3,2,4,3,3,3,4,3,2,4,3,2,4,3,2,3,4,3,1,2 as there should be 25 entries and there are 28 entries.

I am assuming that 4,3,2 is repeated thrice and 1 is extra, but if that's not the case please make sure to calculate your own values keeping in mind my solution. Pkease dont get confused. the solution will remain the same just the numbers would change.

m=25, n= 25, alpha level of .05

  

Our estimate of the pooled sample variance is:

s=0.87939

i) We are testing:

Assuming that the underlying distributions are normal, then under Ho:

The observed value of Test statistic is:

The p-value is .059553.
How to calculate p-value?

You can always calculate p-value from t table but it is a daunting task as degree of freedom = 48 is not given so you can approximately find the p-value or else use approximation formula:

but the best way to get your p-value if you can use EXCEL is to type this formula in any of the cell:

=T.DIST(-1.9298,48,TRUE) This gives the answer 0.029777 But this gives you the probablitiy of one tailed test, we need to calculate for two tailed test hence we'll multiply it with 2

2* 0.029777 = 0.059553= p-value

Since p-value is greater than , we do not have sufficient evidence to reject Ho at 5% level of significance. Lotion A is as effective as Lotion B and there is no difference in both the lotions.