A gastroenterologist conducted an experiment to determine whether infections wit

Question

A gastroenterologist conducted an experiment to determine whether infections with Salmonella stimulates induction of IgG in a mouse model of infection. 26 mice were randomly allocated to two groups of 13 each. In the first group mice were gavaged with 10 cells of S. typhimurium, while mice in the other group only received a placebo. After one week, the total level of IgG (log2) of in each mouse was measured, with the results given below. Salmonella Control 13 20.59 1.13 13 17.78 1.15 Does IgG level depend on treatment? Show your null and alternative hypotheses, your chosen , which test you selected, your calculations of a test statistic, and how you reached your conclusions.

Explanation / Answer

Given that,
mean(x)=20.59
standard deviation , 1 =1.13
number(n1)=13
y(mean)=17.78
standard deviation, 2 =1.15
number(n2)=13
null, Ho: u1 = u2
alternate, H1: 1 != u2
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
zo=20.59-17.78/sqrt((1.2769/13)+(1.3225/13))
zo =6.28
| zo | =6.28
critical value
the value of |z | at los 0.05% is 1.96
we got |zo | =6.284 & | z | =1.96
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 6.28 ) = 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: 1 != u2
test statistic: 6.28
critical value: -1.96 , 1.96
decision: reject Ho
p-value: 0

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