Exercise Set 83 2 Nitrites are often added to meat products

Exercise Set 8.3: 2. Nitrites are often added to meat products as preservatives. In a study of the effect of these chemicals on bacteria, the rate of uptake of a radio - labeled amino acid was measured for a number of cultures of bacteria, some growing in a medium to which nitrites had been added. Here are the summary statistics from this study. Group n x s Nitrite 30 7880 1115 Control 30 8112 1250 Carry out a test of the research hypothesis that nitrites decrease amino acid uptake at the 2% significance leve

Solution

Let X be the Nitrate group
Let Y be the control group

if x - y < 0 then nitrates decrease the number of amino acid uptakes.


The hypothesis test in this question is:

H0: x - y= 0 vs. H1: x - y < 0

sample mean for X =7880 and for Y =8112 and sx^2= sample variance for X =1115^2 =1243225 and sy^2 = sample variance for Y = 1250^2 = 1562500.......sample size=30 FOR both the cases.....
The test statistic is:
z = (( 7880 - 8112 ) - 0 ) / sqrt ( 1243225 / 30 + 1562500 / 30 ) = -0.7586231

The p-value = P( Z < z )
= P( Z < - 0.7586231 )
= 0.2240390

Since the p-value is greater than the significance level of 0.02 we fail to reject the null hypothesis and conclude
x - y = 0 is true i.e nitrates do not decrease the number of amino acid uptakes.....