The U.S. Department of Agriculture publishes statistics on the production of var
ID: 2936655 • Letter: T
Question
The U.S. Department of Agriculture publishes statistics on the production of various types of food commodities by month. Shown here are the production figures on broccoli for January of a recent year through December of the next year. Use these data to compute 12-month centered moving averages (T # C ). Using these computed values, determine the seasonal effects (S # I ).
Month
January (1st year) February March April
May June July August September October November December
Broccoli (million pounds)
132.5 164.8 141.2 133.8 138.4 150.9 146.6 146.9 138.7 128.0 112.4 121.0
Month
January (2nd year) February March April
May June July August September October November December
Broccoli (million pounds)
104.9 99.3 102.0 122.4 112.1 108.4 119.0 119.0 114.9 106.0 111.7 112.3
Explanation / Answer
Given that,
mean(x)=137.933
standard deviation , s.d1=13.9509
number(n1)=12
y(mean)=111
standard deviation, s.d2 =7.1568
number(n2)=12
null, Ho: u1 = u2
alternate, H1: u1 > u2
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.796
since our test is right-tailed
reject Ho, if to > 1.796
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =137.933-111/sqrt((194.62761/12)+(51.21979/12))
to =5.95
| to | =5.95
critical value
the value of |t | with min (n1-1, n2-1) i.e 11 d.f is 1.796
we got |to| = 5.95035 & | t | = 1.796
make decision
hence value of | to | > | t | and here we reject Ho
p-value:right tail - Ha : ( p > 5.9504 ) = 0.00005
hence value of p0.05 > 0.00005,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 > u2
test statistic: 5.95
critical value: 1.796
decision: reject Ho
p-value: 0.00005
we have enough evidence to support the production figures on broccoli for January of a recent year through December of the next year compare both
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