Since the population standard deviation is unknown, the mean follows a t(n-1) distribution.
"H_0 \\mu=50"
"H_a \\mu<50"
"t-value= \\frac{\\bar{X}-\\mu}{\\frac{s}{\\sqrt{n}}}"
"= \\frac{42-50}{\\frac{11.9}{\\sqrt{12}}}=-2.32881"
The critical region (left sided)
Obtained from =T.INV(0.01,11) excel formula.
"t_{(0.01,11)}=-2.7181"
Since absolute t-value (2.33) is less than the absolute critical value (2.72), we fail to reject the null hypothesis and conclude that there is no sufficient evidence to conclude that the mean I less than 50.
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