Solution :
This is the left tailed test,
The null and alternative hypothesis is ,
H0 : = 445
Ha : < 445
s = s2 = 441 = 21
Test statistic = t =
= ( - ) / s / n
= (441 - 445) / 21 / 12
Test statistic = t = -0.660
= 0.025
degrees of freedom = n - 1 = 12 - 1 = 11
P(t < t ) = 0.025
= P(t < -2.201 ) = 0.025
t = -2.201
Reject HO , test statistic > critical value
Reject HO if t < -2.201
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