Question

In Study Design 2, Super Sneaker Company drew at random two groups of 12 high school students from the Halifax school district database. After obtaining their shoe sizes, the company manufactured 12 pairs of shoes for group 1, each pair with both soles constructed from material A, and 12 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.

Using option III, the following data were used to test the hypothesis that wear for material B was greater than wear for material A.

Group 1 - Material A
12.73	9.11	7.39	10.80	8.16	7.87	9.57	9.43	11.77	7.62	8.44	12.33
Group 2 - Material B
10.70	11.09	9.83	9.26	11.39	10.15	8.93	10.57	10.53	9.62	8.62	7.84

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.  [3 pt(s)]

Is this a 1-sided or a 2-sided test?
2-sided
1-sided
[1 pt(s)]

Which interval in the table contains the p-value for the test?
p-value ≤ 0.005
0.005 < p-value ≤ 0.01
0.01 < p-value ≤ 0.025
0.025 < p-value ≤ 0.05
0.05 < p-value ≤ 0.1
p-value > 0.1
[3 pt(s)]

What is the 90% confidence interval for the difference in wear between material B and material A (μ_B − μ_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. Lower bound: ___ Upper bound: ___

Answer 1

Solution: Here concept of two independent samples t-test and concept of confidence interval for difference of population means is used.

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