Quiz 12: Chi-square tests
Question 1
If ,
find .
Your answer is correct.
Use the chi-square
tables with ,
and .
Not correct. Choice (b)
is false.
.
Not correct. Choice (c)
is false.
You have used the
wrong value for .
Not correct. Choice (d)
is false.
.
Question 2
Provide bounds for .
Not correct. Choice (a)
is false.
Try
again.
Not correct. Choice (b)
is false.
You have reversed the upper and lower limits. Obviously
must
exceed 0.025.
Your answer is correct.
Draw a chi-square diagram and mark in the value 38.5 on the
-axis. From the
tables, and
Mark both 37.652 and
40.646 on the -axis as well,
and it will be obvious that
has bounds (0.025, 0.05).
Not correct. Choice (d)
is false.
Draw a chi-square diagram and mark in the value 38.5 on the
-axis. From
the tables,
Now mark 37.652 on your diagram, and it will be obvious that
must
be less than 0.05.
Question 3
Questions 3 to 6 use the same information.
The observed frequencies of genotypes A, B and C of 100 progeny from a genetic cross are : 18, 55 and 27 respectively. A model states that A, B and C occur in the ratio 1:2:1.
Under the model, the expected frequencies () are:
The observed frequencies of genotypes A, B and C of 100 progeny from a genetic cross are : 18, 55 and 27 respectively. A model states that A, B and C occur in the ratio 1:2:1.
Under the model, the expected frequencies () are:
Not correct. Choice (a)
is false.
The
frequencies must satisfy .
Your answer is correct.
Under the model, the proportions for A, B and C are respectively
.
Multiplying by 100 gives the expected frequencies 25, 50, 25.
Not correct. Choice (c)
is false.
These are not
in the correct order.
Not correct. Choice (d)
is false.
These are not in the correct order.
Question 4
Questions 3 to 6 use the same information.
The observed frequencies of genotypes A, B and C of 100 progeny from a genetic cross are : 18, 55 and 27 respectively. A model states that A, B and C occur in the ratio 1:2:1.
Writing for the corresponding expected frequencies under the model, calculate , the observed value of the chi-square test statistic.
The observed frequencies of genotypes A, B and C of 100 progeny from a genetic cross are : 18, 55 and 27 respectively. A model states that A, B and C occur in the ratio 1:2:1.
Writing for the corresponding expected frequencies under the model, calculate , the observed value of the chi-square test statistic.
Not correct. Choice (a)
is false.
You have found
.
Your answer is correct.
.
Not correct. Choice (c)
is false.
Check your calculations.
Not correct. Choice (d)
is false.
. You have
found instead, .
Question 5
Questions 3 to 6 use the same information.
The observed frequencies of genotypes A, B and C of 100 progeny from a genetic cross are : 18, 55 and 27 respectively. A model states that A, B and C occur in the ratio 1:2:1.
State the appropriate chi-square variable, , for testing the goodness of fit of this model.
The observed frequencies of genotypes A, B and C of 100 progeny from a genetic cross are : 18, 55 and 27 respectively. A model states that A, B and C occur in the ratio 1:2:1.
State the appropriate chi-square variable, , for testing the goodness of fit of this model.
Your answer is correct.
There are three
categories, so .
Not correct. Choice (b)
is false.
Try again. There
are three categories
Not correct. Choice (c)
is false.
where
is the
number of categories.
Not correct. Choice (d)
is false.
There
are 3 categories, not 100.
Question 6
Questions 3 to 6 use the same information.
The observed frequencies of genotypes A, B and C of 100 progeny from a genetic cross are : 18, 55 and 27 respectively. A model states that A, B and C occur in the ratio 1:2:1.
Test the model for goodness of fit, providing an expression for the P-value.
The observed frequencies of genotypes A, B and C of 100 progeny from a genetic cross are : 18, 55 and 27 respectively. A model states that A, B and C occur in the ratio 1:2:1.
Test the model for goodness of fit, providing an expression for the P-value.
Not correct. Choice (a)
is false.
You have used the wrong chi-square distribution.
Not correct. Choice (b)
is false.
You have used the wrong chi-square distribution.
Not correct. Choice (c)
is false.
The P-value is not the lower tail of
.
Your answer is correct.
Since there are 3 categories and since
, the appropriate
chi-square distribution is
and P-value = .
This means that the data are fairly typical of what is expected under the model.
Question 7
Questions 7 to 10 use the same information.
A market researcher wishes to assess consumers’ preference among four different colours available on a name-brand dishwasher. In a sample of 198 recent sales, 61 were for stainless steel, 55 for white, 41 for black and 41 for cream.
To test the hypothesis that all four colours are equally preferred, a chi-square test is used. Writing for the corresponding expected frequencies under the model, calculate , the observed value of the chi-square test statistic.
A market researcher wishes to assess consumers’ preference among four different colours available on a name-brand dishwasher. In a sample of 198 recent sales, 61 were for stainless steel, 55 for white, 41 for black and 41 for cream.
To test the hypothesis that all four colours are equally preferred, a chi-square test is used. Writing for the corresponding expected frequencies under the model, calculate , the observed value of the chi-square test statistic.
Your answer is correct.
.
Not correct. Choice (b)
is false.
Check your
calculations.
Not correct. Choice (c)
is false.
Check your caluclations.
Not correct. Choice (d)
is false.
You have
found
instead of
Question 8
Questions 7 to 10 use the same information.
A market researcher wishes to assess consumers’ preference among four different colours available on a name-brand dishwasher. In a sample of 198 recent sales, 61 were for stainless steel, 55 for white, 41 for black and 41 for cream.
To test the hypothesis that all four colours are equally preferred, a chi-square test is used. Write an expression for the P-value.
A market researcher wishes to assess consumers’ preference among four different colours available on a name-brand dishwasher. In a sample of 198 recent sales, 61 were for stainless steel, 55 for white, 41 for black and 41 for cream.
To test the hypothesis that all four colours are equally preferred, a chi-square test is used. Write an expression for the P-value.
Not correct. Choice (a)
is false.
You have used the wrong chi-square distribution.
Your answer is correct.
Under this
model, the are
all 49.5, and .
Since there are 4 categories, the appropriate chi-square is
, and P-value
=
Not correct. Choice (c)
is false.
Check your
caluclation of .
Not correct. Choice (d)
is false.
Try again. You have used the wrong chi-square distribution.
Question 9
Questions 7 to 10 use the same information.
A market researcher wishes to assess consumers’ preference among four different colours available on a name-brand dishwasher. In a sample of 198 recent sales, 61 were for stainless steel, 55 for white, 41 for black and 41 for cream.
Writing for the expected frequencies under a model which states that the preferences are in the ratio 6:5:4:3, calculate , the observed value of the chi-square test statistic.
A market researcher wishes to assess consumers’ preference among four different colours available on a name-brand dishwasher. In a sample of 198 recent sales, 61 were for stainless steel, 55 for white, 41 for black and 41 for cream.
Writing for the expected frequencies under a model which states that the preferences are in the ratio 6:5:4:3, calculate , the observed value of the chi-square test statistic.
Not correct. Choice (a)
is false.
You have found
instead of
Not correct. Choice (b)
is false.
The
expected frequencies under this model are 66, 55, 44, 33. Using these, recalculate
.
Not correct. Choice (c)
is false.
. You have
found instead, .
Your answer is correct.
The expected frequencies under this model are 66, 55, 44, 33 (for example
the model indicates that the proportion preferring stainless steel is
Multiplying by 198 gives 66. similarly for the other three colours.
Thus, .
Thus, .
Question 10
Questions 7 to 10 use the same information.
A market researcher wishes to assess consumers’ preference among four different colours available on a name-brand dishwasher. In a sample of 198 recent sales, 61 were for stainless steel, 55 for white, 41 for black and 41 for cream.
To test the hypothesis that the preferences are in the ratio 6:5:4:3, a chi-square test is used. Write an expression for the P-value.
A market researcher wishes to assess consumers’ preference among four different colours available on a name-brand dishwasher. In a sample of 198 recent sales, 61 were for stainless steel, 55 for white, 41 for black and 41 for cream.
To test the hypothesis that the preferences are in the ratio 6:5:4:3, a chi-square test is used. Write an expression for the P-value.
Your answer is correct.
Under this model,
the are respectively
66, 55, 44, 33 and .
Since there are 4 categories, the appropriate chi-square is
and the P-value
is .
Not correct. Choice (b)
is false.
Check your
caluclation of .
Not correct. Choice (c)
is false.
Check
your caluclation of .
Not correct. Choice (d)
is false.
You have used the wrong chi-square distribution.










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