An advertisement for a certain brand of cigarettes claimed that on average there's no more than 18mg of nicotine per cigarettes . A test of 12 cigarettes gave a sample mean of 19.1 . Assuming varience is 4 , test the claim with a significance level of α = 0.05

My ans is

Ho =µ_0 =18

H1 =µ_0 <18Since n < 30 , and standard deviation of population unknown , so , i use t-distribution

t test = (19.1-18) / ( 2 /sqrt(2) ) = 1.905

t α = 0.05 , v =11 = 1.796

Since t test > t critical , so i reject the Ho , but accroding to the ans , i should not reject the Ho ,

Is my ans wrong ?