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

critical value is 2.236
test statistic = (obs-exp)/SE
(104-100)/(10/sqrt(25))
test statistic of 2.

Ho: U=100
Ha: U>100
U=average weight for the population of product X

A test statistic of 2 is too close for a .01 significance level. (more than 1% outside 2SD)