A manufacturer of flashlight batteries took a sample of 8 batteries from a day’s production and used them continuously until they were drained. The number of hours they were used until failure was
342 426 545 364 451 631 512 492
Assuming that the numbers of hours are approximately normally distributed, find the 95% confidence interval for the mean of the number of hours of all the batteries until they fail.
If one tests whether the mean of the number of hours of all the batteries until they fail is 500 or not at 0.05, would the null hypothesis be rejected? Justify your answer based on the confidence interval obtained.