Question

In: Statistics and Probability

Personnel in a consumer testing laboratory are evaluating the absorbency of paper towels. They wish to...

Personnel in a consumer testing laboratory are evaluating the absorbency of paper towels. They wish to compare a set of Walmart generic brand towels to similar group of BOUNTY name brand towels. For each brand they dip one towel into a tub of fluid, allow the paper to drain back into the vat for two minutes, and then determine the amount of liquid the paper has taken up from the vat. A random sample of 9 Walmart generic brand towels has a mean of 6.44 milliliters with a standard deviation of 3.32 milliliters. A random sample of 12 Bounty Brand towels hand sample mean of 9.42 milliliters with a standard deviation of 1.621 milliliters. Use the .10 significance to test if there is a difference in the mean amount of liquid absorbed by the two paper towels. Assume the population standard deviations are not equal.

1. State the Null and Alternate Hypothesis(H0, H1).

2. Determine the level of significance.

3. Determine the test statistic. (z or t)

4. State the decision rule.(Reject H0 if)

5. Conduct the test and make a decision.(Include Formula and show all work)

6. Interpret the results.

"PLEASE SHOW ALL WORK WITH THE CORRECT ANSWERS"

Thanks!

Solutions

Expert Solution

(1)   null hypothesis H0:µwalmart=µbounty and alternate hypothesis H1:µwalmart ≠ µbounty

(2) level of significance (alpha)=0.10

(3)here we use t-test with

(4) reject H0 if t > 1.729

the two tailed critical value is t(0.1/2,19)=1.729

(5)statistic t=|(mean1-mean2)|/((sp*(1/n1 +1/n2)1/2) =2.7224

with df is n=n1+n2-2 =19and sp2=((n1-1)s12+(n2-1)s22)/n=6.1623

since the calculated t=2.7224 belongs to critical region , so we reject the null hypothesis

(or p-value is less than level of significance alpha=0.1, so we reject H0)

t-test
sample mean s s2 n (n-1)s2
walmart 6.4400 3.3200 11.0224 9 88.1792
bounty 9.4200 1.6210 2.6276 12 28.9041
difference= 2.9800 sum= 13.6500 21 117.0833
sp2= 6.1623
sp= 2.4824
SE= 1.0946
t= 2.7224
two tailed p-value= 0.0135
two tailed critical t(0.1/2) 1.7291

(6) since we reject the null hypothesis and we may interpret as  there is a difference in the mean amount of liquid absorbed by the two paper towels.

orchestra answered 1 year ago
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