(solution) An RCMP officer would like to estimate the true mean speed of all

(solution) An RCMP officer would like to estimate the true mean speed of all

An RCMP officer would like to estimate the true mean speed of all vehicles along a particular stretch of highway.  She measures the speeds of a simple random sample of 52 vehicles and calculates a mean speed of 112.16 km/h.  The population standard deviation of speeds is known to be 12.95 km/h.

(a)  What is a 97% confidence interval for the true mean speed of all vehicles on the highway?

(b) What is a 99% confidence interval for the true mean speed of all vehicles on this highway?

(c)  When the confidence level increases, What happens to the length of the confidence interval? Does it increase or decrease?