Let X 1 , X 2 , X 3 , X 4 , X 5 be a random sample from a N(, 1) distribution, where

Let X₁, X₂, X₃, X₄, X₅ be a random sample from a N(μ, 1) distribution, where μ is unknown. Suppose that we have observed the following values 

5.45, 4.23, 7.22, 6.94, 5.98

We would like to decide between

a. Define a test statistic to test the hypotheses and draw a conclusion assuming α = 0.05.

b. Find a 95% confidence interval around X̅. Is μ₀ included in the interval? How does the exclusion of μ₀ in the interval relate to the hypotheses we are testing?

Ho: = = 5, H: + 5.