15. (10 pts) An engineering company claims to have produced a longer lasting D battery with an average life span of 16.2 hours with a standard deviation of 0.75 hours. An independent testing firm randomly selected 30 of these new D batteries and found the sample mean life span was 15.9 hours. What is the probability of getting a random sample of 30 batteries in which the sample mean life span is 15.9 hours or less? Based on this probability, is the engineering company’s claim reasonable (be sure to state why and show your work)? Round your probability to THREE decimal places.
16. (10 pts) A company has initiated a training program for new hires. After surveying 16 new employees, they determined the average training time was 7 hours with a sample standard deviation of 2 hours. Assume that the underlying population is normally distributed. Show your work and round your CI to THREE decimal places.
a. Define the random variable X for this problem in words.
b. Define the random variable 𝑋̅ in words.
c. Construct a 90% confidence interval for the population mean length of time of new hire training.
d. Why does the error bound change if the confidence level is increased to 95%?
e. Which interval is more precise, 90% or 95% (and state why)?
17. (10 pts) A researcher randomly surveyed 400 high school students and determined 335 stated they have a mobile phone. We are interested in the population proportion of students who have mobile phones.
a. Define the random variable X for this problem in words.
b. Define the random variable P’ in words.
c. Construct a 99% confidence interval for the population proportion of high school students who claim to have a mobile phone. Round your CI to THREE decimal places.
d. Calculate the error bound.
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