Question

3. (20pts) The Food and Drug Administration (FDA) has established an upper tolerance of 5 parts per billion for the cancer-causing substance nitrosamine in beer. Suppose that Pabst and Miller are identified by the FDA as containing excessive concentrations of nitrosamines and are tested by an independent testing agency with the results shown in the accompanying table (in parts per billion). Also suppose that 36 bottles were randomly selected from each brand. Stat. Pabst Miller -------- ----- ------ Mean 5.25 5.31 Std. Dev. 1.20 1.44 Specify the null and alternative hypotheses. What are the test statistics for these tests?

Answer 1

Solution:

Independent two samples t test

= 5.25 ,   = 5.31

s₁ = 1.20 , s₂ = 1.44

n₁ = 36 , n₂ = 36

The test statistic t is given by

t =

where    denotes the pooled variance.

t =   

=

t = -0.192055   

Test statistic t =   -0.192055