Understanding t vs z Confidence Intervals
Describe the conditions under which a t-based confidence interval should be used instead of a z-based interval when estimating a population mean. In your description, discuss the assumptions regarding the population standard deviation and sample size.
Comparing Confidence Intervals for Different Levels
Consider a scenario where a population standard deviation is known. Part (a): Derive the formulas for the 90% and 95% confidence intervals for the population mean using the Z-distribution. Part (b): Compare the widths of these intervals and explain which is wider and why. Part (c): Discuss how increasing the confidence level affects the margin […]
Part a
Derive the formulas for the 90% and 95% confidence intervals for the population mean using the Z-distribution. Include the use of critical z-values in your derivation.
Assessing Conditions for a Z-confidence Interval for a Mean
A factory produces metal rods, and the quality control manager aims to estimate the average rod length using a Z-confidence interval. It is known that the population standard deviation is known. State and explain the two key conditions that must be satisfied to validly apply a Z-based confidence interval for the mean.