Personnel in a consumer testing laboratory are evaluating th

Personnel in a consumer testing laboratory are evaluating the absorbency of paper towels. They wish to compare a set of store brand towels to a similar group of name brand ones. For each brand, they dip a ply of the paper into a tub of fluid, allow the paper to drain back into the vat for two minutes, and then evaluate the amount of liquid the paper has taken up from the vat. A random sample of 9 store brand paper towels absorbed the following amounts of liquid in milliliters:

8, 8, 3, 1, 9, 7, 5, 5, 12

An independent random sample of 12 name brand towels absorbed the following amounts of liquid in milliliters:

12, 11, 10, 6, 8, 9, 9, 10, 11, 9, 8, 10

Use the 0.10 significance level and test if there is a difference in the mean amount of liquid absorbed by the two types of paper towels. (Hint: use t-test)

Solution

calculate mean and median for both set of data

set 1 = mean =  6.44 , s.d = 3.32

set 2 = mean = 9.417 s.d = 1.621

Step 1: State the null and alternate hypotheses.

H0: m1 = m2     

H1: m1 m2

Step 2: State the level of significance.

The .10 significance level is stated

in the problem.

Step 3:   Find the appropriate test statistic.

We will use unequal variances t-test

Variable samle size mean standard devaiation

Store 9 6.44 3.32

name 12 9.417 1.621

T test = ( x1 - x2 )/ root (s1^2 / n1) + (s2^2 / n2) = 6.44 - 9.417 / root (3.32)^2 / 9 + (1.621)^2 / 12) = -2.478

Df = 9 + 12 - 2 = 19

Step 4: State the decision rule.

Reject H0 if

t > ta/2d.f. or t < - ta/2,d.f.

t > t.05,10 or t < - t.05, 10

t > 1.328 or t < -1.328

Step 5: Compute the value of t and make a decision

The computed value of t is less than the lower critical value, so our decision is to reject the null hypothesis. We conclude that the mean absorption rate for the two towels is not the same