Answer: u = (3.1645, 2.8355)
Step-by-step explanation:
Constructing a 90% confidence interval for population mean (u) is given by
u = x + Zα/2 * σ/√n or u = x - Zα/2 * σ/√n
u = population mean
x = sample mean = 3
σ = population standard deviation = √0.09= 0.3
The question gave us variance and standard deviation = √variance.
Zα/2= z score for a two tailed test at level of significance α = 1.645 ( for a 90% confidence level)
For the upper limit
u = 3 + 1.645 * (0.3/√9)
u = 3 + 1.646 * (0.3/3)
u = 3 + 1.645 * (0.1)
u = 3 + 0.1645
u = 3.1645
For lower limit
u = 3 - 1.645 * (0.3/√9)
u = 3 - 1.646 * (0.3/3)
u = 3 - 1.645 * (0.1)
u = 3 - 0.1645
u = 2.8355
Hence the interval for population mean at 95% confidence level is
u = (3.1645, 2.8355)
