Based on a random sample of 25 units of product X the averag

Based on a random sample of 25 units of product X, the average weight is 104 lbs. and the sample standard deviation is 10 lbs. We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lbs. (assume the population is normally distributed). Form the hypotheses according to the question and perform the test at 1% significance level.
Show the calculated value of the test statistic and the critical value (given in terms of the value of the test statistic) at a = 0.01.

Solution

Let mu be the population mean

The test hypothesis:

Ho: mu=100 (i.e. null hypothesis)

Ha: mu>100 (ie. alternative hypothesis)

The test statistic is

Z=(xbar-mu)/(s/vn)

=(104-100)/(10/sqrt(25))

=2
It is a right-tailed test.

Given a=0.01, the critical value is Z(0.01) =2.33 (from standard normal table)

The rejection region is if Z>2.33, we reject the null hypothesis.

Since Z=2 is less than 2.33, we do not reject the null hypothesis.

So we can not conclude that the average weight for the population of product X is greater than 100 lbs.