Never Ready batteries claim to have a mean lifetime of 8 hours and come from a Normal population. A quality control supervisor selects a simple random sample of n=18 batteries and measures the lifetime of each. The sample mean is 8.25 with a standard deviation of 0.3. She is curious to see if the mean lifetime for the batteries differs from 8 hours. Test the supervisor’s claim at the 0.01 significance level. a)State and define the parameter. b)State the null and alternative hypothesis. c)List and support any conditions that need to be met in order to conduct the test. d)Conduct the test. State the p-value. e)Interpret the p-value in the context of the problem. f)State a conclusion and write what this mean in the context of the problem. g)What type of error could you have just made? Again state what this means in context. h)Construct a 99% confidence interval from the sample data. How would you come to the same conclusion as you did in part f)?.