A manufacturer producing ball bearings claims that the mean weight of ball bearings produced is 5 ounces. The distribution is known to be normal with standard deviation 0.1 ounces. A random sample of 16 ball bearings is taken and their mean weight is found to be 5.038 ounces.
(a) test at the 5% level of significance the null hypothesis that the population mean weight is 5 ounces against the alternative that it is bigger.
(b) Test at 10% level of significance
(c) Test at the 5% level of significance if the mean weight is no more than 5 ounces
(d) Find the p-value of the test