According to the census bureau, 3.13 people reside in the typical american household a residents per household was 2.86 residents. The standard deviation of this sample was 1.30 residents . At the 0.05 significance level, is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.13 persons.

What I got is .4505 P value and to reject the hypothesis . Hoping you could tell me if i am wrong and brief explanation on how to use z table or when to use t vs z table would be nice .