Question

find confidence intervals for with asymptotic level 90% using both the "solving" and the plug-in methods. Use n = 25, and Xn = 45. (Enter your answers accurate to 4 decimal places. Use the Gaussian estimate q₀.₀₅ ≈ 1.96 for best results.)

Answer 1

To find a 90% confidence interval using an n of 25 and an Xn of 45, apply the 'solving' or 'plug-in' method with the appropriate Z-value of 1.645 for a 90% confidence interval, not the 1.96 which would be for a 95% interval.

Step-by-step explanation:

The question involves finding confidence intervals at a 90% level using the sample mean (Xn) and sample size (n). The two methods mentioned are the 'solving' method and the 'plug-in' method, both of which essentially require the use of the standard normal distribution and the provided sample statistics to calculate the interval.

For the 'solving' method, you would start with the formula for the confidence interval for the mean, which is Xn ± Z*(σ/√n), where Z* is the Z-value for the desired confidence level. Since the population standard deviation (σ) is not provided, we assume the sample standard deviation approximates it, or if this problem pertains to proportions, σ would be the standard error based on the proportion. With n = 25 and Xn = 45, and using the Z-value for a 90% confidence interval (Z* ≈ 1.645, not 1.96 which is for a 95% interval), you plug the numbers in to calculate the interval.

For the 'plug-in' method, you would typically use a calculator or statistical software, entering the known values and letting the software compute the confidence interval.

The provided examples demonstrate how to use a calculator to find confidence intervals for different scenarios, but do not directly apply to the given problem.