Question

1A) The corrosive effects of various soils on coated and uncoated steel pipe was tested by using a dependent sampling plan. The data collected are summarized below, where d is the amount of corrosion on the coated portion subtracted from the amount of corrosion on the uncoated portion. Does this random sample provide sufficient reason to conclude that the coating is beneficial? Use α = 0.01 and assume normality.

n = 47, Σd = 221, Σd² = 6166

(a) Find t. (Give your answer correct to two decimal places.)


(b) Find the p-value. (Give your answer correct to four decimal places.)

1B) Twenty laboratory mice were randomly divided into two groups of 10. Each group was fed according to a prescribed diet. At the end of 3 weeks, the weight gained by each animal was recorded. Do the data in the following table justify the conclusion that the mean weight gained on diet B was greater than the mean weight gained on diet A, at the α = 0.05 level of significance? Assume normality. (Use Diet B - Diet A.)

Diet A	12	7	9	12	10	7	9	9	6	5
Diet B	14	23	12	10	10	19	21	20	18	15

(a) Find t. (Give your answer correct to two decimal places.)


(b) Find the p-value. (Give your answer correct to four decimal places.)

Answer 1

1a)

here dbar = Σd /n=221/47=4.702

and std deviation =sqrt(( Σd² -( Σd)²/n)/(n-1))=sqrt((6166-(221)²/47))/46)=10.557

a)test statisitc t =dbar*sqrt(n)/std deviation =4.702*sqrt(47)/10.557=3.05

b) p value =0.0019

1B)

a)

t =3.86

b)

p value =0.0019