Question

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, as in the first design.

Group 1 - Material A 17.92 13.91 12.01 15.78 12.86 12.54 14.42 14.26 16.86 12.27 13.17 17.48 14.74 13.94 16.73 16.30

Group 2 - Material B 15.52 15.95 14.55 13.92 16.28 14.91 13.56 15.37 15.33 14.33 13.22 12.35 17.83 14.20 14.49 16.20

1. How many degrees of freedom are associated with the test statistic?

2. What is the 99% confidence interval for the difference in wear between material B and material A (?B ? ?A)? 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.

Answer 1

= 14.6994

s1 = 1.93

 = 14.8756

s2 = 1.35

1) df = (s1^2/n1 + s2^2/n2)^2/(s1^2/n1)^2/(n1 - 1) + (s2^2/n2)^2/(n2 - 1))

= ((1.93)^2/16 + (1.35)^2/16)^2/(((1.93)^2/16)^2/15 + ((1.35)^2/16)^2/15) = 27

2) At 99% confidence interval the critical value is t^* = 2.771

The 99% confidence interval is

() +/- t^* * sqrt(s1^2/n1 + s2^2/n2)

= (14.6994 - 14.8756) +/- 2.771 * sqrt((1.93)^2/16 + (1.35)^2/16)

= -0.1762 +/- 1.63163

= -1.80783, 1.45543