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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. State the null hypothesis and the alternate hypothesis.

b. Show the decision rule graphically. Use the .05 significance level.

c. Compute the value of t. What is your decision regarding the null hypothesis? Briefly summarize your results.

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