P-value from simple random sample

Question

Assume that a simple random sample has been selected from a normally distributed population. Find the P-value for a claim of 𝜇 = 5. Express answer to 3 decimal places.

Sample data: n = 81, x = 5.25, s = 2.60, 𝛼 = 0.01.

Answer 1

State null and alternate hypotheses

H₀: µ=5

H_a: µ≠5

Calculate z-statistic

Z = (x̄-µ)/(s/√n)

Z = (5.25-5)/(2.60/√81)

Z ≈ 0.87

Calculate p-value

P(Z<-0.87) + P(Z>0.87) = 2•P(Z>0.87) = 2(0.1922) = 0.3844 ≈ 0.384

As 0.384>α, we fail to reject the null hypothesis. This means that we are 99% confident that the true population mean is 5.

Hope this helped! The answer in bold is the p-value.