Final answer:
The appropriate test for the hypothesis that the new battery has a greater mean life than the older version is a One-sample z-test for a population mean. This is applicable when the population standard deviation is known and the sample size is large. Alternately, if the population standard deviation were unknown or the sample size was small, a One-sample t-test for a population mean would be used.
Step-by-step explanation:
The appropriate test for the researchers' hypothesis that the mean battery life of their new battery is greater than the known mean life of the older version would be A. One-sample z-test for a population mean. This is because the standard deviation of the population is known and the sample size is sufficiently large (n ≥ 30), allowing for the Central Limit Theorem to apply. The z-test is used when the population standard deviation is known, and the research entails comparing the sample mean to the population mean.
If the sample standard deviation were used instead, or if the population was known to not follow a normal distribution and the sample size was small, a B. One-sample t-test for a population mean would be the proper choice. This test is utilized when the population standard deviation is unknown and is based on the t-distribution, which adjusts for smaller sample sizes and is more conservative than the z-distribution.
The other options, such as a test for a population proportion or a matched-pairs test, are not suitable for this scenario as they are not relevant to testing a hypothesis about a population mean. Remember, when dealing with means, the focus is on differences in central tendencies, not proportions or matched pairs.