1. Automatic shutoff valves contain sensors that cut off water ow in the event of a leak, thereby preventing ooding. One important characteristic is the time (in milliseconds) required for the sensor to detect the water leak. Sample data obtained for four different shutoff valves are available in the data set \"Valves.\" (a) Construct and conduct an appropriate hypothesis test to determine if the mean detection times differ among the four valve models. Use a 5% level of signicance. (b) Which valve(s) would you recommend to a client? Why? (c) Are your conclusions robust to a change in the assumptions, namely that the populations variances are not equal? Explain.