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 50 vehicles and calculates a mean speed of 112.8 km/h. The population standard deviation of speeds is known to be 14.3 km/h.

(a) Calculate a 94% confidence interval for the true mean speed of all vehicles on the highway.

(b) Provide an interpretation of the interval in (a).

(c) Calculate a 99% confidence interval for the true mean speed of all vehicles on this highway.

(d) What happens to the length of the confidence interval when the confidence level increases? (Does it increase or decrease?)