Compute the value of t and conclude with the result.
The mean life of a battery used in a digital clock is 305 days. The lives of the batteries follow the normal distribution. The battery was recently modified with the objective of making it last longer. A sample of 20 of the modified batteries had a mean life of 311 days with a standard deviation of 12 days. Did the modification increase the mean life of the battery?
a. declare the null hypothesis and the alternate hypothesis.
b. illustrate the decision rule graphically. Use the .05 significance level.
c. multiply the value of t. What is your decision regarding the null hypothesis? Briefly summarize your results.