You are conducting a multinomial hypothesis test (αα = 0.05) for the claim that all 5 categories are equally likely to be selected. Complete the table.
Category | Observed Frequency |
Expected Frequency |
Squared Pearson Residual |
---|---|---|---|
A | 21 | ||
B | 12 | ||
C | 16 | ||
D | 8 | ||
E | 24 |
Report all answers accurate to three decimal places. But
retain unrounded numbers for future calculations.
What is the chi-square test-statistic for this data? (Report answer
accurate to three decimal places, and remember to use the unrounded
Pearson residuals in your calculations.)
χ2=χ2=
What are the degrees of freedom for this test?
d.f.=
What is the p-value for this sample? (Report answer accurate to
four decimal places.)
p-value =
It may be best to use the =CHIDIST() function in Excel to do
this calculation.
The p-value is...
This test statistic leads to a decision to...
As such, the final conclusion is that...
Observed (Oi ) | Expected ( Ei) | Oi-Ei | (Oi-Ei)^2 | (Oi-Ei)^2/Ei |
21 | 16.2 | 4.8 | 23.04 | 1.4222 |
12 | 16.2 | -4.2 | 17.64 | 1.0889 |
16 | 16.2 | -0.2 | 0.04 | 0.0025 |
8 | 16.2 | -8.2 | 67.24 | 4.1506 |
24 | 16.2 | 7.8 | 60.84 | 3.7556 |
observed frequncies are Oi
21 12 16 8 24
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expected frequencies are Ei = (21 + 12 + 16 + 8 + 24)/5 =
16.2
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and claiming hypothesis is
null, Ho: all 5 categories are equally likely to be selected.
alternative, H1: all 5 categories are not equally likely to be
selected.
level of significance, alpha = 0.05
from standard normal table, chi square value at right tailed, ᴪ^2
alpha/2 =9.4877
since our test is right tailed,reject Ho when ᴪ^2 o >
9.4877
we use test statistic ᴪ^2 o = Σ(Oi-Ei)^2/Ei
from the table take sum of (Oi-Ei)^2/Ei, we get ᴪ^2 o =
10.4198
critical value
the value of |ᴪ^2 alpha| at los 0.05 with d.f, n - 1 = 5 - 1 = 4 is
9.4877
we got | ᴪ^2| =10.4198 & | ᴪ^2 alpha | =9.4877
make decision
hence value of | ᴪ^2 o | > | ᴪ^2 alpha| and here we reject
Ho
ᴪ^2 p_value =0.0339
----------------------------------------------------------------------------------------
What is the chi-square test-statistic for this data? test
statistic: 10.4198
What are the degrees of freedom for this test? d.f =
4
What is the p-value for this sample? p-value = 0.0339
The p-value is...? less than (or equal to) αα
This test statistic leads to a decision to...? reject the
null
As such, the final conclusion is that...
There is sufficient evidence to warrant rejection of the claim that
all 5 categories are equally likely to be selected.
You are conducting a multinomial hypothesis test (αα = 0.05) for the claim that all 5...
You are conducting a multinomial hypothesis test (αα = 0.05) for the claim that all 5 categories are equally likely to be selected. Category Observed Frequency A 20 B 15 C 15 D 12 E 18 What is the chi-square test-statistic for this data? χ2=χ2= What are the degrees of freedom for this test? d.f. = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to)...
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