hypothesis test

[shadow turtle]

Suppose that the following data are obtained by randomly sampling 8 samples from a population with distribution N(μ,0.5^2).

4.7, 4.9, 5.2, 4.8, 4.9, 5.1, 4.5, 4.7 (sample mean 4.85)

Answer the questions below.

1. H0 : μ = 5.2, H1 : μ ≠5.2, α = 0.05 (Reject or accept H0).
2. H0 : μ = 5.0, H1 : μ ≠5.0, α = 0.05 (reject or accept H0).
3. Find the 95% confidence interval for μ (find the endpoints to three decimal places).

My answer is

1. t= (4.85-5.2)/(0.5/sqrt(8)) = -1.980

Because -1.980 < 1.96 , then accept H0.

2. Accept H0

3. 4.504 <= μ <= 5.196

Is my answer correct?

[valid cedar]

1. Wait patiently for a helper to come along.
2. Once someone helps you, say thank you and close the thread with: ```diff
   +close

[manic spear]

@shadow turtle This is a two tailed test therefore your null hypothesis acceptance interval is $(-1.96, 1.96)$ therefore the answer to the first is reject H0.