A survey of 144 retail stores revealed that the average price of a DVD was $375 with a standard error of $20. If 95% and 98% confidence intervals were developed to estimate the true cost of the DVD, what differences would they have?
A) Standard errors
B) Interval widths
C) Z-values
D) Both standard errors and interval widths
E) Both interval widths and Z-values

Question

Quizplus · Accepted Answer

The differences between the 95% and 98% confidence intervals would be in the interval widths and the Z-values. The Z-value changes because it is dependent on the level of confidence chosen; a 95% confidence interval uses a Z-value of approximately 1.96, while a 98% confidence interval uses a higher Z-value, typically around 2.33. This change in Z-value affects the width of the confidence interval, making the 98% confidence interval wider than the 95% confidence interval. The standard error remains the same in both cases as it is a measure of the variability of the sample mean and is not affected by the confidence level.

A Survey of 144 Retail Stores Revealed That the Average