Question: a). Explain, using examples, why conducting a significance test for a claim is always a one-tail test?

b). the mass of an item manufactured is known to be normally distributed with a standard deviation of 5 grams?

In a recent survey, 16 items were randomly selected and were found to have a mean mass of 200 grams.

i. Calculate a 99% confidence intervals for the mean mass of all the items manufactured, assuming that the standard deviation remain at 5 grams.

ii. If we want to estimate the mean with ± 1, 5 grams at 99% confidence level and the standard remains at 5 grams, calculate the least sample size.

b). A certain electrical item is known to have a life span of 20,000 hours of usage. However, it has been recently redesigned to improve on its life span. A random sample of 49 such items were tested and found to have a mean life span of 22,000 hours with a standard deviation of 4,000 hours.

Test at 1% level whether the new design has significantly increased the life span.