In 1973, the effects of vitamin C on the incidence of colds was studied at a Nav
ID: 3365274 • Letter: I
Question
In 1973, the effects of vitamin C on the incidence of colds was studied at a Navajo boarding school. Daily pills of vitamin C were given to 400 children, while placebos that were identical in taste and color were given to 401 children. They found that 330 of those that took the vitamin C pill were not absent for illness over the test period and that only 303 of those that received the placebo had no sick days. Perform a test to see if there is a statistic improvement in attendance rate for the vitamin C test group. (Use alpha = 0.05) *PLEASE ANSWER USING A TI-84 CALCULATOR
Explanation / Answer
This is a difference in the propotions test
so
Since the null hypothesis states that P1=P2, we use a pooled sample proportion (p) to compute the standard error of the sampling distribution.
p = (p1 * n1 + p2 * n2) / (n1 + n2)
where p1 is the sample proportion from population 1, p2 is the sample proportion from population 2, n1 is the size of sample 1, and n2 is the size of sample 2.
putting the values
p1 = 330/400 = 0.825
p2 = 303/401 = 0.755
p = (p1 * n1 + p2 * n2) / (n1 + n2)
= (0.825*400 + 0.755*401)/(400+401) = 0.789
Compute the standard error (SE) of the sampling distribution difference between two proportions.
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
where p is the pooled sample proportion, n1 is the size of sample 1, and n2 is the size of sample 2.
SE = sqrt( 0.789 * ( 1 - 0.789 ) * [ (1/400) + (1/401) ] )
= 0.028
The test statistic is a z-score (z) defined by the following equation.
z = (p1 - p2) / SE
(0.825-0.755)/0.028
= 2.5
we check the p value from the z table as
P ( Z>2.5 )=1P ( Z<2.5 )=10.9938=0.0062
as the p value is less than alpha = 0.05 , Hence the results are signficant and we can say that there is a statistic improvement in attendance rate for the vitamin C test group