deg of freedom = 12
Here Ha: mue1 -mue 2 <0. Means mue 1 < mue 2
Therefore we are dealing with single tail probability.
Now test statistic with 12 degrees of freedom is -1.85. According to t Table 1. It lies between .05 and .025 p value. By Interpolation we get p =0.037 for single tail.
Answer: p- value 0.037
Please note that the p- value is not an exact value because t table was used for interpolation.
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