Question

Consider a multinomial experiment with *n* = 307 and
*k* = 4. The null hypothesis to be tested is
*H*_{0}: *p*_{1} =
*p*_{2} = *p*_{3} =
*p*_{4} = 0.25. The observed frequencies resulting
from the experiment are: **(You may find it useful to
reference the appropriate table: chi-square tableor F
table)**

Category | 1 | 2 | 3 | 4 |

Frequency | 85 | 58 | 89 | 75 |

**b-1.** Calculate the value of the test statistic.
**(Round intermediate calculations to at least 4 decimal
places and final answer to 3 decimal places.)**

Answer #1

any query, please ask

Consider a multinomial experiment with n = 275 and k = 4. The
null hypothesis to be tested is H0: p1 = p2 = p3 = p4 = 0.25. The
observed frequencies resulting from the experiment are: (You may
find it useful to reference the appropriate table: chi-square table
or F table)
Category 1 2 3
4
Frequency 67 55 75
78
a. Choose the appropriate alternative hypothesis.
Not all population proportions are equal to 0.25.
All population proportions differ...

Consider a multinomial
experiment with n = 350 and k = 3. The null
hypothesis is H0: p1 =
0.60, p2 = 0.30, and p3 =
0.10. The observed frequencies resulting from the experiment are:
(You may find it useful to reference the appropriate table:
chi-square table or F table)
Category
1
2
3
Frequency
216
100
34
a.
Choose the appropriate alternative hypothesis.
All population proportions differ from their hypothesized
values.
At least one of the population proportions differs...

You are conducting a multinomial Goodness of Fit hypothesis test
for the claim that the 4 categories occur with the following
frequencies:
HoHo :
pA=0.4pA0.4; pB=0.25pB0.25; pC=0.25pC0.25; pD=0.1pD0.1
Complete the table. Report all answers accurate to two decimal
places, unless otherwise specified.
Category
Observed
Frequency
Expected
Frequency
A
39
B
18
C
30
D
7
What is the chi-square test-statistic for this data? (Round to two
decimal places)
χ2=χ2
What is the P-Value? (Round to four decimal places)
P-Value =

You are conducting a multinomial Chi-Square Goodness of Fit
hypothesis test for the claim that the 4 categories occur with the
following frequencies:
HoHo : pA=0.1; pB=0.5; pC=0.1; pD=0.3
Complete the table. Report all answers accurate to three decimal
places.
Category
Observed
Frequency
Expected
Frequency
A
17
B
25
C
6
D
16
What is the chi-square test-statistic for this data?
χ2=
What is the P-Value?
P-Value =

You are conducting a multinomial Goodness of Fit hypothesis test
for the claim that the 4 categories occur with the following
frequencies:
HoHo :
pA=0.1pA0.1; pB=0.5pB0.5; pC=0.3pC0.3; pD=0.1pD0.1
Complete the table. Report all answers accurate to three decimal
places.
Category
Observed
Frequency
Expected
Frequency
A
23
B
54
C
37
D
8
What is the chi-square test-statistic for this data?
χ2=
What is the P-Value?
P-Value =
For significance level alpha 0.01,
What would be the conclusion of this hypothesis test?
Reject the...

Suppose that a response can fall into one of k = 5 categories
with probabilities p1, p2, , p5 and that n = 300 responses produced
these category counts.
Category 1 2 3 4 5
Observed Count 46 63 73 52 66
(a) Are the five categories equally likely to occur? How would
you test this hypothesis?
H0: At least one pi is different from 1 5 . Ha: p1 = p2 = p3 =
p4 = p5 = 1...

You are conducting a multinomial Goodness of Fit hypothesis test
for the claim that the 4 categories occur with the following
frequencies:
Ho: pA=0.3; pB=0.1; pC=0.4; pD=0.2
Complete the table. Report all answers accurate to three decimal
places.
Category
Observed
Frequency
Expected
Frequency
A
52
B
34
C
52
D
37
What is the chi-square test-statistic for this data? (2 decimal
places)
χ2=
What is the P-Value? (3 decimal places)
P-Value =
For significance level alpha 0.1,
What would be...

A multinomial experiment produced the following results:
Category
1
2
3
Frequency
139
120
71
a.
Choose the appropriate alternative hypothesis at
H0: p1 = 0.40,
p2 = 0.40, and p3 =
0.20.
All population proportions differ from their hypothesized
values.
At least one of the population proportions differs from its
hypothesized value.
b.
Calculate the value of the test statistic at
H0: p1 = 0.40,
p2 = 0.40, and p3 = 0.20....

Birds use color to select and avoid certain types of food. The
authors of a particular article studied the pecking behavior of
1-day-old bobwhites. In an area painted white, they inserted four
pins with different colored heads. The color of the pin chosen on
the bird's first peck was noted for each of 34 bobwhites, resulting
in the accompanying table.
Color
First
Peck
Frequency
Blue
15
Green
9
Yellow
7
Red
3
Do these data provide evidence of a color...

The authors of a paper concerned about racial stereotypes in
television counted the number of times that characters of different
ethnicities appeared in commercials aired on a certain city's
television stations, resulting in the data in the accompanying
table.
Ethnicity
African-
American
Asian
Caucasian
Hispanic
Observed Frequency
60
10
324
6
Based on the 2000 Census, the proportion of the U.S. population
falling into each of these four ethnic groups are 0.177 for
African-American, 0.032 for Asian, 0.734 for Caucasian,...

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