Is there a difference in the amount of airborne bacteria between carpeted and un
ID: 3330203 • Letter: I
Question
Is there a difference in the amount of airborne bacteria between carpeted and uncarpeted rooms? In an experiment, five rooms were carpeted and five were left uncarpeted. The rooms are similar in size and function. After a suitable period of time, the concentration of bacteria in the air was measured (in units of bacteria per cubic foot) in all of these rooms. The data and summaries are provided: 184 Carpeted rooms: Uncarpeted rooms: Reference: Ref 17-3 27.0 172 7.9 Based on the analysis above, which of the following is a reasonable conclusion? Select one: a. There is evidence (P> 0.40) that the mean bacterial concentration in carpeted rooms is greater than that in uncarpeted rooms. O b. There is very little evidence (P0.05) that the mean bacterial concentration in carpeted rooms is greater than that in uncarpeted rooms. c. There is evidence (P 0.40) that the mean bacterial concentration in carpeted rooms is greater than that in uncarpeted rooms.Explanation / Answer
Given that,
mean(x)=184
standard deviation , s.d1=27
number(n1)=5
y(mean)=172
standard deviation, s.d2 =17.9
number(n2)=5
null, Ho: u1 = u2
alternate, H1: u1 < u2
level of significance, = 0.05
from standard normal table,left tailed t /2 =2.132
since our test is left-tailed
reject Ho, if to < -2.132
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =184-172/sqrt((729/5)+(320.41/5))
to =0.828
| to | =0.828
critical value
the value of |t | with min (n1-1, n2-1) i.e 4 d.f is 2.132
we got |to| = 0.82831 & | t | = 2.132
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value:left tail - Ha : ( p < 0.8283 ) = 0.77297
hence value of p0.05 < 0.77297,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 < u2
test statistic: 0.828
critical value: -2.132
decision: do not reject Ho
p-value: 0.77297
there is evidence (p >0.40) that the mean bacterial concentration in carpeted rooms is greater than the uncarpeted rooms
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.