Question

**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, 15 high school students were
drawn at random from the Halifax School District database. After
obtaining their shoe sizes, the company manufactured 15 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.**

**After 3 months, the amount of wear in each shoe was
recorded in standardized units as follows:**

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |

A | 12.43 | 9.34 | 7.88 | 10.78 | 8.54 | 8.29 | 9.73 | 9.61 | 11.61 | 8.08 | 8.77 | 12.08 | 9.98 | 9.37 | 11.51 |

B | 10.95 | 11.28 | 10.21 | 9.73 | 11.54 | 10.48 | 9.45 | 10.84 | 10.81 | 10.04 | 9.18 | 8.52 | 12.73 | 9.94 | 10.16 |

What is the test statistic value to a minimum of 5 decimal places? (not pooled, I don't believe)

Answer #1

A |
B |
Difference |

12.43 | 10.95 |
1.48 |

9.34 | 11.28 |
-1.94 |

7.88 | 10.21 |
-2.33 |

10.78 | 9.73 |
1.05 |

8.54 | 11.54 |
-3 |

8.29 | 10.48 |
-2.19 |

9.73 | 9.45 |
0.28 |

9.61 | 10.84 |
-1.23 |

11.61 | 10.81 |
0.8 |

8.08 | 10.04 |
-1.96 |

8.77 | 9.18 |
-0.41 |

12.08 | 8.52 |
3.56 |

9.98 | 12.73 |
-2.75 |

9.37 | 9.94 |
-0.57 |

11.51 | 10.16 |
1.35 |

Sample mean of the difference using excel function AVERAGE(),
x̅_{d} = -0.524

Sample standard deviation of the difference using excel function
STDEV.S(), s_{d} = 1.90464

Sample size, n = 15

Test statistic:

t = (x̅_{d})/(s_{d}/√n) = (-0.524)/(1.90464/√15)
= **-1.06552**

---------------------------

If you have any doubt ask in comments.

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 2, Super Sneaker Company drew at random two
groups of 16 high school students from the Halifax school district
database. After obtaining their shoe sizes, the company
manufactured 16 pairs of shoes for group 1, each pair with both
soles constructed from material A, and 16 pairs of shoes for group
2, each pair with both soles constructed from material B. After 3
months, the amount of sole wear in each shoe was recorded in
standardized units,...

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