Question: Past records show that the mean life of a certain brand of batteries used in a digital clock is 305 days. The battery was recently modified to last longer. A sample of 20 of the modified batteries had a mean life of 311 days with a sample standard deviation of 12 days. Did the modification increase the mean life of the battery? Assume that the population distribution of battery life is normally distributed and use a 5% level of significance. The null hypothesis is that the mean life is still no greater than 305 days.