Question

# Suppose you want to determine whether the brand of laundry detergent used and the temperature affects...

Suppose you want to determine whether the brand of laundry detergent used and the temperature affects the amount of dirt removed from your laundry. You buy two different Brand of Detergent (A and B) and choose three different Temperature (cold, warm and hot). Four laundry loads were washed for each combination of detergent and temperature. The amount of dirt removed from each load was recorded. The partial ANOVA table is given below.

 Source DF SS MS F Brand (a) 20 20 ? Temperature (b) 80 40 ? Brand* Temperature (c) 30 15 ? Error (d) 72 4 Total (e) 202

Fill in DF in the ANOVA table.

(a) = 1, (b) = 2, (c) = 2, (d) = 1, (e) = 6

(a) = 1, (b) = 2, (c) = 2, (d) = 18, (e) = 23

(a) = 2, (b) = 3, (c) = 6, (d) = 13, (e) = 24

(a) = 2, (b) = 3, (c) = 6, (d) = 1, (e) = 12

Continue to consider Question 14.

State the null and alternative hypotheses if you want to test if there is an interaction effect between the brand of detergent and the temperature in the mean amount of removed dirt.

H0: There is an interaction between brands and temperatures; Ha: There is no interaction between brands and temperatures

H0: mu1=mu2=mu3, Ha: At least two mu’s are different

H0: There is no interaction between brands and temperatures; Ha: There is an interaction between brands and temperatures

H0: muA=muB, Ha: muA is not equal to muB

Continue to consider Question 14.

Find the value of test statistic of the test in Question 15.

A. 3.75

B. 5

C. 4

D. 10

Continue to consider Question 14.

Using a 0.10 level of significance, find rejection region.

F > 3.10

F > 8.53

F > 2.62

F > 9.00

Continue to consider Question 14.

What is your conclusion at 0.10 level of significance?

A. Reject H0. Sufficient evidence of an interaction between brands and temperature.

B. Do not reject H0. Insufficient evidence of a difference between two brands of detergent.

C. Reject H0. Sufficient evidence of a difference between two brands of detergent.

D. Do not reject H0. Insufficient evidence of an interaction between brands and temperature.

 Source df SS MS F A 1 20 20.00 5.00 B 2 80 40.00 10.00 A*B 2 30 15.00 3.75 error 18 72 4.00 total 23 202

a)

(a) = 1, (b) = 2, (c) = 2, (d) = 18, (e) = 23

H0: There is no interaction between brands and temperatures; Ha: There is an interaction between brands and temperatures

value of test statistic of the test =3.75

rejection region : F > 2.62

C. Reject H0. Sufficient evidence of a difference between two brands of detergent.

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