You are conducting a multinomial Goodness of Fit hypothesis test for the claim t
ID: 3316397 • Letter: Y
Question
You are conducting a multinomial Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies:
HoHo : pA=0.2; pB=0.2; pC=0.3; pD=0.3
Complete the table. Report all answers accurate to three decimal places.
What is the chi-square test-statistic for this data?
2=2=
What is the P-Value?
P-Value =
For significance level alpha 0.1,
What would be the conclusion of this hypothesis test?
Reject the Null Hypothesis
Fail to reject the Null Hypothesis
Category ObservedFrequency Expected
Frequency A 17 B 33 C 32 D 39
Explanation / Answer
observed frequncies are Oi
17 33 32 39
------------------------------------------------------------------
expected frequencies are Ei
0.2*sum(17+33+32+39) = 24.2
0.2*sum(17+33+32+39) = 24.2
0.3*sum(17+33+32+39) = 36.3
0.3*sum(17+33+32+39) = 36.3
------------------------------------------------------------------
and claiming hypothesis is
null, Ho: proportion are equal acorss
alternative, H1: atleast one proportion is different among them
level of significance, = 0.1
from standard normal table, chi square value at right tailed, ^2 /2 =4.6052
since our test is right tailed,reject Ho when ^2 o > 4.6052
we use test statistic ^2 o = (Oi-Ei)^2/Ei
from the table take sum of (Oi-Ei)^2/Ei, we get ^2 o = 6.0523
critical value
the value of |^2 | at los 0.1 with d.f, n - 1 = 3 - 1 = 2 is 4.6052
we got | ^2| =6.0523 & | ^2 | =4.6052
make decision
hence value of | ^2 o | > | ^2 | and here we reject Ho
^2 p_value =0.0485
ANSWERS
---------------
null, Ho: proportion are equal acorss
alternative, H1: atleast one proportion is different among them
test statistic: 6.0523
critical value: 4.6052
p-value:0.0485
decision: reject Ho
Observed (Oi ) Expected ( Ei) Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 17 24.2 -7.2 51.84 2.1421 33 24.2 8.8 77.44 3.2 32 36.3 -4.3 18.49 0.5094 39 36.3 2.7 7.29 0.2008Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.