Question

A parking control officer is conducting an analysis of the amount of time left on parking meters. A quick survey of 30 cars that have just left their metered parking spaces was recorded (in minutes). The sample mean and standard deviation are calculated as minutes and minutes. Use the t-distribution to construct a confidence interval for the mean amount of time left for all city's meters. For part (a), round your answer to 3 decimal places. (a) What is the critical value that will need to be used to calculate the confidence interval? For parts (b) and (c), round your answers to 2 decimal places. (b) What is the margin of error? (c) What is the confidence interval?

Answer 1

To construct a confidence interval for the mean amount of time left for all city's meters, you need to use the t-value and calculate the degrees of freedom. The margin of error can be calculated using the standard deviation and critical value, and the confidence interval is determined by adding and subtracting the margin of error from the sample mean.

Step-by-step explanation:

To construct a confidence interval for the mean amount of time left for all city's meters, the critical value that needs to be used is the t-value. The critical value is determined by the desired level of confidence, degrees of freedom, and the t-distribution. In this case, the degrees of freedom (df) can be calculated as n-1, where n is the sample size.

(b) To calculate the margin of error, we need the standard deviation of the sample and the critical value. The margin of error can be calculated as the product of the critical value and the standard deviation divided by the square root of the sample size.

(c) The confidence interval can be calculated by subtracting the margin of error from the sample mean and adding the margin of error to the sample mean.