A consumer electronics firm has developed a new type of remote control button that is designed to operate longer before becoming intermittent. A random sample of 35 of the new buttons is selected and each is tested in continuous operation until becoming intermittent. The resulting lifetimes are found to have a sample mean of xx =1,241.1 hours and a sample standard deviation of s = 108.6.

(a) Independent tests reveal that the mean lifetime (in continuous operation) of the best remote control button on the market is 1,200 hours. Letting be the mean lifetime of the population of all new remote control buttons that will or could potentially be produced, set up the null and alternative hypotheses needed to attempt to provide evidence that the new button's mean lifetime exceeds the mean lifetime of the best remote button currently on the market.

(b) Using the previously given sample results, use critical values to test the hypotheses you set up in part a by setting equal to .10, .05, .01, and .001. What do you conclude for each value of ? (Round your answers to 3 decimal places.)