1. Perform the indicated goodness-of-fit
test.
Using the data below and a 0.05 significance level, test the claim
that the responses occur with percentages of 15%, 20%, 25%, 25%,
and 15% respectively.
a. test statistic
b. critical value
2.Perform the indicated goodness-of-fit
test.
In studying the responses to a multiple-choice test question, the
following sample data were obtained. At the 0.05 significance
level, test the claim that the responses occur with the same
frequency.
a. test statistic
b. critical value
1)
applying chi square goodness of fit test: |
|||||
relative | observed | Expected | residual | Chi square | |
category | frequency(p) | Oi | Ei=total*p | R2i=(Oi-Ei)/√Ei | R2i=(Oi-Ei)2/Ei |
A | 0.150 | 12.000 | 12.000 | 0.00 | 0.000 |
B | 0.200 | 15.000 | 16.000 | -0.25 | 0.063 |
C | 0.250 | 16.000 | 20.000 | -0.89 | 0.800 |
D | 0.250 | 18.000 | 20.000 | -0.45 | 0.200 |
E | 0.150 | 19.000 | 12.000 | 2.02 | 4.083 |
total | 1.000 | 80 | 80 | 5.146 |
a)
test statistic X2 = | 5.146 |
b)
for 0.05 level and 4 degree of freedom :rejection region = | 9.488 |
2)
applying chi square goodness of fit test: |
relative | observed | Expected | residual | Chi square | |
category | frequency(p) | Oi | Ei=total*p | R2i=(Oi-Ei)/√Ei | R2i=(Oi-Ei)2/Ei |
A | 0.200 | 12.000 | 16.000 | -1.00 | 1.000 |
B | 0.200 | 15.000 | 16.000 | -0.25 | 0.063 |
C | 0.200 | 16.000 | 16.000 | 0.00 | 0.000 |
D | 0.200 | 18.000 | 16.000 | 0.50 | 0.250 |
E | 0.200 | 19.000 | 16.000 | 0.75 | 0.563 |
total | 1.000 | 80 | 80 | 1.875 |
a)
test statistic X2 = | 1.875 |
b)
for 0.05 level and 4 degree of freedom :rejection region = | 9.488 |
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