Question

Given that a 95% confidence interval is (6.5, 12.5), we can state that there is a 95% probability that the true population mean is between 6.5 and 12.5

Answer 1

Let
μ = population mean
σ = population std. deviation.
n = sample size.

At 95% confidence level, the confidence interval is
(μ - 1.96y, μ + 1.96y),
where y = σ/√n.

Therefore
μ - 1.96y = 6.5 (1)
μ + 1.96y = 12.5 (2)

Add (1 and (2) to obtain
2μ = 19
μ = 9.5

The calculated value of μ is within the interval (6.5, 12.5).

Answer:
The statement "There is a 95% probability that the true population mean is between 6.5 and 12.5" is True.