The marketing department for a hand calculator claims the battery pack performs 20,000 calculations before it has to be recharged. The quality control manager for the manufacturer is entrusted with validating the claim that the battery pack works as long as the specifications state in order to secure a large order from a key customer. A test of 114 battery packs yields an average of 19,695 calculations with a standard deviation of 1,103. 1) Formulate the appropriate null and alternative hypotheses.
2) Calculate the appropriate test statistic and p-value.
3) How is the p-value computed for a two-sided alternative given a null hypothesis H0 : μ = μ0 for the mean of a normal distribution with known variance?