The Wimbledon Championships tennis tournament, where women players curtsy to the Queen and fans eat strawberries and cream, finishes in the first week of July. Each match is played on a grass court,...

The Wimbledon Championships tennis tournament, where women players curtsy to the Queen and fans eat strawberries and cream, finishes in the first week of July. Each match is played on a grass court, as opposed to a clay or hard court. Some people believe the grass court is more challenging and speeds up the game. Random samples of match lengths (in minutes) from Wimbledon and from the U.S. Clay Court Championships were obtained. The data are summarized in the table below.

Assume the underlying distribution of match lengths is normal on grass and on clay.

 a. Find a 99% confidence interval for the true mean match length for grass courts at Wimbledon.

b. Find a 99% confidence interval for the true mean match length for clay courts at the U.S. Clay Court Championships.

c. Is there any evidence to suggest the mean match time for grass courts and clay courts is different? Justify your answer.