Question

In Study Design 2, Super Sneaker Company drew at random two groups of 10 high school students from the Halifax school district database. After obtaining their shoe sizes, the company manufactured 10 pairs of shoes for group 1, each pair with both soles constructed from material A, and 10 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, as in the first design.

Group 1 - Material A
12.18 8.02 6.04 9.96 6.93 6.60 8.55 8.38 11.08 6.31
Group 2 - Material B
10.12 10.57 9.12 8.46 10.91 9.49 8.09 9.97 9.93 8.88

1. Assume the standard deviation of wear is the same for both materials A and B. Calculate the test statistic. Use at least 5 digits to the right of the decimal.
2. Which interval in the table contains the p-value for the test?
3. What is the 99% confidence interval for the difference in wear between material B and material A (μB − μA)? Use software to get a more precise critical value, but confirm it's roughtly the same value you get from the table. Use at least 5 digits to the right of the decimal. Lower bound: Upper bound:

Answer 1