Exit A water quality engineer collects 26 samples at Site A and 50 samples at Si
ID: 3064033 • Letter: E
Question
Exit A water quality engineer collects 26 samples at Site A and 50 samples at Site B. She takes the samples back to the lab and finds that 40% and 52% of the samples at Sites A and B, respectively, violate the water quality criterion for enterococci bacteria. Based on these results and accepting a probability a 0.01 of a Type l error, what is the measured test statistic and are the probabilities of violating the water quality criterion for enterococci bacteria the same or different at these two sites?Explanation / Answer
Given that,
sample one, x1 =10.4, n1 =26, p1= x1/n1=0.4
sample two, x2 =26, n2 =50, p2= x2/n2=0.52
null, Ho: p1 = p2
alternate, H1: p1 != p2
level of significance, = 0.01
from standard normal table, two tailed z /2 =2.576
since our test is two-tailed
reject Ho, if zo < -2.576 OR if zo > 2.576
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.4-0.52)/sqrt((0.479*0.521(1/26+1/50))
zo =-0.993
| zo | =0.993
critical value
the value of |z | at los 0.01% is 2.576
we got |zo| =0.993 & | z | =2.576
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -0.9935 ) = 0.3205
hence value of p0.01 < 0.3205,here we do not reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 != p2
test statistic: -0.993
critical value: -2.576 , 2.576
decision: do not reject Ho
p-value: 0.3205
decision
+/-0.993, same
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