Question

A random sample of 49 measurements from a population with population standard deviation σ₁ = 5 had a sample mean of x₁ = 9. An independent random sample of 64 measurements from a second population with population standard deviation σ₂ = 6 had a sample mean of x₂ = 12. Test the claim that the population means are different. Use level of significance 0.01.

(a) Compute the corresponding sample distribution value. (Test the difference μ₁ − μ₂. Round your answer to two decimal places.)
(b) Find a 99% confidence interval for μ₁ − μ₂.

(Round your answers to two decimal places.)

lower limit
upper limit

Can you please explain how to get the μ₁ − μ_{2 and the upper/lower limit}

Answer 1

Since, the interval does not include zero in it, hence we reject Ho.

Conclusion: Reject Ho. Therefore, we conclude that there is enough evidence to support the claim that the two population means are significantly different.