How to quickly to get the SD and P-value by hand written. Plz give me some advis

Question

How to quickly to get the SD and P-value by hand written. Plz give me some advise.

Super Sneaker Company is evaluating two different materials, A and B, to be used to construct the soles of their new active shoe targeted to city high school students in Canada. While material B costs less than material A, the company suspects that mean wear for material B is greater than mean wear for material A. Two study designs were initially developed to test this suspicion. In both designs, Halifax was chosen as a representative city of the targeted market. In Study Design 1, 9 high school students were drawn at random from the Halifax School District database. After obtaining their shoe sizes, the company manufactured 9 pairs of shoes, each pair with one shoe having a sole constructed from material A and the other shoe, a sole constructed from material B. The researcher in charge of this design asked the company to randomly assign material A to the right shoe or to the left shoe, for each of the 9 pairs. Why? Incorrect Right shoe wear is always less than left shoe wear Correct: Right shoe wear is generally different than left shoe wear. Incorrect Right shoe wear is always greater than left shoe wear. [1 pt(s)] You are correct. Computer's answer now shown above Previous Tries Your receipt no s 157-294 After 3 months, the amount of wear in each shoe was recorded in standardized units as follows: 1 2 3 5 6 7 9 A 17.06 12.49 10.32 14.62 11.29 10.93 13.07 12.89 15.85 B 14.53 15.02 13.42 12.70 15.40 13.83 12.29 14.36 14.31

Explanation / Answer

here we use t-test and let alpha=0.05

H0:meanA=meanB

H1:meanA<meanB

t=(mean1-mean2)/((sp*(1/n1 +1/n2)1/2) and sp2=((n1-1)s12+(n2-1)s22)/n and with df is n=n1+n2-2

t=(13.17-13.98)/(1.77*(1/9+1/9))=-2.06 with 16 df

sp2=3.1329

one tailed p-value=0.028 ( using ms-excel comman=tdist(2.06,16,1)) is less than alpha=0.05 ,

so we fail to accept null hypothesis H0 and conclude that mean wear for material B is greater than mean wear for material A

for sd use ms-excel command=stdev()

s.n. A B 1 17.06 14.53 2 12.49 15.02 3 10.32 13.42 4 14.62 12.7 5 11.29 15.4 6 10.93 13.83 7 13.07 12.29 8 12.89 14.36 9 15.85 14.31 mean 13.16889 13.98444 s2 5.205286 1.060528 n 9 9

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