Question

Suppose that random samples Y₁, Y₂, ..., Y₉ are obtained from a normal distribution with an unknown mean μ and variance σ² = 4. Find a 90% confidence interval for μ.

Answer 1

To find a 90% confidence interval for the population mean μ, you can use the formula CI = (sample mean) ± (critical value) * (standard error). Since the sample sizes is greater than 30 and the population standard deviation σ is known, you can use the z-distribution to find the critical value for a 90% confidence level. Plug in the values to calculate the confidence interval.

Step-by-step explanation:

To find a 90% confidence interval for the population mean μ, we can use the formula:

CI = (sample mean) ± (critical value) * (standard error)

Since the sample sizes is greater than 30 and the population standard deviation σ is known, we can use the z-distribution to find the critical value for a 90% confidence level. The critical value for a 90% confidence interval is approximately 1.645.

The standard error can be calculated as σ / sqrt(n), where σ is the population standard deviation and n is the sample size. In this case, σ = 2 (since σ² = 4) and n = 9.

So the confidence interval for μ is:

(sample mean) ± 1.645 * (2 / sqrt(9))

Simplifying this, we get:

(sample mean) ± 1.645 * 0.667

This gives us the 90% confidence interval for μ.