Hello I need help with errors type please help

Question

1) Given a sample X₁, ... , X_n from X ~ N (𝜇, 𝜎²), we want to test H₀ : 𝜇 = 1 against H₁ : 𝜇 ≠ 1. If X̅ = 1.2, n = 9, and S = 0.2 T = ?, df = ?

2) For question 1, what type of errors do we make? (𝛼 = 0.05)

Answer 1

1) t = (x-bar - µ₀) / (s/√n) = (1.2 - 1) / (.2/√9) = 3

df - n-1 = 8

p-value = P(t ≥ 3 or t ≤ -3) = 0.017

2) Since our p-value of 0.017 is less than ∝ = 0.05, we would reject the null hypothesis. This means that we could make a Type I error - we conclude that the population mean is not equal to 1 when it actually is equal to 1.

If you have any questions, message me on Wyzant :-).