Question

Using the previous part, find confidence intervals for a with asymptotic level 90% using both the "solving" and the "plug-in" methods. Use n = 25, and X₁ = 4.5.

(Enter your answers accurate to 2 decimal places. Use the Gaussian estimate 90.05≈ 1.6448 for best results.)
Isolve = ___
Iplug-in = ___

Answer 1

To find the confidence intervals for a with asymptotic level 90% using both the "solving" and the "plug-in" methods, we can use the given information and formulas.

Step-by-step explanation:

To find the confidence intervals for a with asymptotic level 90% using both the "solving" and the "plug-in" methods, we can use the given information. The solving method involves calculating the confidence interval by solving a mathematical equation. The plug-in method involves plugging in the values into a formula.

For the solving method, we can use the formula: CI = X₁ ± Z * σ / √n, where X₁ is the sample mean, Z is the Z-score corresponding to the confidence level, σ is the population standard deviation, and n is the sample size.

For the plug-in method, we can use the formula: CI = X₁ ± Z * s / √n, where X₁ is the sample mean, Z is the Z-score corresponding to the confidence level, s is the sample standard deviation, and n is the sample size.

Plugging in the given values (X₁ = 4.5, n = 25), using the Gaussian estimate 90.05 ≈ 1.6448 for the Z-score, and calculating the standard deviation or sample standard deviation based on the information provided, we can find the confidence intervals using both methods.

The solving method will give us the confidence interval (I_solve) and the plug-in method will give us the confidence interval (I_plug-in).