# In Study Design 2, Super Sneak

In Study Design 2, Super Sneaker Company drew at randomtwo groups of 12 high school students from the Halifax schooldistrict database. After obtaining their shoe sizes, the companymanufactured 12 pairs of shoes for group 1, each pair with bothsoles constructed from material A, and 12 pairs of shoes for group2, each pair with both soles constructed from material B. After 3months, the amount of sole wear in each shoe was recorded instandardized units, as in the first design.

Using option III, the following data were used to test thehypothesis that wear for material B was greater than wear formaterial 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 bothmaterials A and B. Calculate the test statistic. Use at least 5digits to the right of the decimal.  [3 pt(s)]

Is this a 1-sided or a 2-sided test?2-sided1-sided[1 pt(s)]

Which interval in the table contains the p-value for thetest?p-value ≤ 0.0050.005 < p-value ≤ 0.010.01 < p-value ≤ 0.0250.025 < p-value ≤ 0.050.05 < p-value ≤ 0.1p-value > 0.1[3 pt(s)]

What is the 90% confidence interval for the difference in wearbetween material B and material A (μB −μA)? Use software to get a more precisecritical value, but confirm it’s roughtly the same value you getfrom the table.  Use at least 5 digits to the right ofthe decimal. Lower bound: ___ Upper bound: ___

Solution: Here concept of two independent samples t-test andconcept of confidence interval for difference of population meansis used.

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