Could someone show me how to do this problem step by step Sh

Could someone show me how to do this problem step by step?

Should the statistician use a t distribution, a normal distribution, or neither to test the null hypothesis?

mean for data set is 3.36, s is 0.376 and n = 55. the data is approximately normal and standard deviation is unknown. H0: mean =3.326 H1: mean does not equal 3.326

I said normal but the answer is t distribution.

Solution

Even is standard deviation is unkown, CLT can be used as sample size is greater than 55, and thus we can use normal distribution. But some authors prefer t distribution even when sample size is greater than 30. Both normal and t is correct depending upon the explanation used.