Question 1

Two allergists recorded the main area of allergy for new patients during a month. At $\alpha = 0.05$, test the claim that the allergy diagnosis and the doctor that treated the patients at independent.
$\begin{array} { l c c c c } \text { Allergies } & \text { Pollen } & \text { Food } & \text { Mold } & \text { Pets } \ \text { Doctor } 1 & 7 & 7 & 8 & 8 \ \text { Doctor } 2 & 26 & 7 & 10 & 24 \end{array}$

Accepted Answer

A)  There is evidence to reject the claim that the allergy diagnosis and the doctor are not related because the trest value 15.507 > 1.980 
B)  There is not evidence to reject the claim that the allergy diagnosis and the doctor are not related because the test value 1.980 > 15.507 
C)  There is evidence to reject the claim that the allergy diagnosis and the doctor are not related because the test value 7.815 > 5.908 
D)  There is not evidence to reject the claim that the allergy diagnosis and the doctor are not related because the test value 5.908 < 7.815

Question 2

A random group of students was selected from a large student conference to analyze their class in school. Is there evidence to reject the hypothesis that the number of students is equally distributed between the four classes, at $\alpha = 0.05 ?$
$\begin{array} { l c c c c } \text { Year in school } & \text { Freshman } & \text { Sophomore } & \text { Junior } & \text { Senior } \ \text { Number of students } & 12 & 12 & 13 & 23 \end{array}$

Accepted Answer

A)  There is evidence to reject the claim that students are equally distributed between the four classes because the test value 7.815 > 5.733 
B)  There is not evidence to reject the claim that students are equally distributed between the four classes because the test value 5.733  5.733 
D)  There is not evidence to reject the claim that the customers' preferences are distributed between the four classes because the test value 5.733 < 9.488

Question 3

The computational procedure for the homogeneity of proportions differs from that of the
test of independence in that it takes into account the standard deviation.

Accepted Answer

A) True 
 B)False

Question 4

The formula for finding the chi-square test value is .

Accepted Answer

The answer of The formula for finding the chi-square test...

Question 5

The following table presents the numbers of cucumber seeds, by brand, that germi failed to germinate 14 days after planting.
$\begin{array}{ccccc}
\hline & \text { Brand A } & \text { Brand B } & \text { Brand C } & \text { Brand D } \
\hline \text { Germinated } & 40 & 37 & 41 & 42 \
\text { Failed to Germinate } & 17 & 14 & 15 & 7 \
\hline
\end{array}$

Can you conclude that the the germination rate is related to the brand of seed? Usi $\alpha = 0.01$ level of significance.

Accepted Answer

The answer of The following table presents the numbers of...

Question 6

A biologist had mice and rats run through a maze and recorded the number that finished the maze successfully and the number that did not. The table lists the results of the study. At $\alpha = 0.05$, test the claim that the rodent type and the success of finishing the maze are nc related.
$\begin{array} { l c c } & \text { Mice } & \text { Rats } \ \text { Finished } & 22 & 28 \ \text { Did not Finish } & 30 & 11 \end{array}$

Accepted Answer

A)  There is evidence to reject the claim that the rodent type and the success of finishing the maze are not related because the test value 3.841  3.841 
C)  There is evidence to reject the claim that the rodent type and the success of finishing the maze are not related because the test value 2.382  2.382

Question 7

The method that uses the formula $\chi ^ { 2 } = \sum \frac { ( | O - E | - 0.5 ) ^ { 2 } } { E }$
is called the________ correction for continuity.

Accepted Answer

The answer of The method that uses the formula \(\chi...

Question 8

A contingency table has 5 rows and 4 columns. How many degrees of freedom are there?

Accepted Answer

A)  12 
B)  16 
C)  20 
D)  15

Question 9

A study was performed at a university to analyze whether the preference for hamburgers or fried chicken is related to the gender of the student. This table lists the results of the study. At $\alpha = 0.05$, test the claim that the meal preference and the gender of the student a related.
$\begin{array} { l c c } & \text { Hamburgers } & \text { Fried Chicken } \ \text { Female } & 11 & 26 \ \text { Male } & 15 & 20 \end{array}$

Accepted Answer

A)  There is evidence to reject the claim that the meal preference and the gender of the student are not related because the test value 3.841 > 1.343 
B)  There is not evidence to reject the claim that the meal preference and the gender of the student are not related because the test value 1.138 < 9.488 
C)  There is not evidence to reject the claim that the meal preference and the gender of the student are not related because the test value 9.488 < 1.138 
D)  There is not evidence to reject the claim that the meal preference and the gender of the student are not related because the test value 1.343 < 3.841

Question 10

If the null hypothesis is not rejected, it can be assumed the proportions are 67)
and the differences in them are due to chance.

Accepted Answer

The answer of If the null hypothesis is not rejected,...

Question 11

An assumption for the goodness-of-fit test is that the frequency for
each category must be five or more.

Accepted Answer

The answer of An assumption for the goodness-of-fit test is...

Question 12

A biology professor claims that, on the average, $15 \%$ of her students get a grade of $A$, $25 \%$ get a B, $40 \%$ get a C , $10 \%$ get a D, and $10 \%$ get an $\mathrm { F }$. The grades of a random sample of 131 students were recorded. The following table presents the results.
$\begin{array}{c|lllll}
\text { Grade } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Observed } & 13 & 21 & 73 & 11 & 13
\end{array}$

What is the value of $\chi ^ { 2 }$ ?

Accepted Answer

A)  14.902 
B)  9.488 
C)  11.143 
D)  16.873

Question 13

Following are observed frequencies. The null hypothesis is $H _ { 0 } : p _ { 1 } = 0.35 , p _ { 2 } = 0.2$, $p _ { 3 } = 0.15 , p 4 = 0.15 , p _ { 5 } = 0.15$.
$\begin{array}{l|lllll}
\text { Category } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Observed } & 38 & 26 & 22 & 4 & 16
\end{array}$

Compute the value of $\chi ^ { 2 }$.

Accepted Answer

A)  14.332 
B)  13.277 
C)  15.086 
D)  12.356

Question 14

A product testing laboratory selected a sample of 20 printers from 2 different manufacturers to determine if they could print more than 100,000 pages without breaking down. At $\alpha = 0.05$, test the claim that the proportions lasting more than 100,000 pages are equal.
$\begin{array} { l c c } & \text { Manufacturer 1 } & \text { Manufacturer 2 } \ \text { Lasted past } 100,000 & 14 & 7 \ \text { Did not last to } 100,000 & 6 & 13 \ \text { Total } & 20 & 20 \end{array}$

Accepted Answer

A)  There is evidence to reject the claim that the proportions are equal because the test value 4.912  1.404 
C)  There is evidence to reject the claim that the proportions are equal because the test value 4.912 > 3.841 
D)  There is not evidence to reject the claim that the proportions are equal because the test value 3.841 > 1.404

Question 15

In a chi-square goodness-of-fit test when there is close agreement between the observed
frequency and the expected frequency, the chi-square test value will be small.

Accepted Answer

A) True 
 B)False

Question 16

A quality control supervisor selected a sample of 100 electronic components from each of three different production chains to determine if the production chains had the same rates of meeting their quality standards. At $\alpha = 0.05$, test the claim that the proportions ar equal.
$\begin{array} { l c c c } \text { Components } & \text { Chain 1 } & \text { Chain 2 } & \text { Chain 3 } \ \text { Meets the standard } & 80 & 87 & 74 \ \text { Does not meet the standard } & 20 & 13 & 26 \ \text { Total } & 100 & 100 & 100 \end{array}$

Accepted Answer

A)  There is not evidence to reject the claim that the proportions are equal because the test value 5.359  5.359 
D)  There is not evidence to reject the claim that the proportions are equal because the test value 5.991 > 5.359

Question 17

The chi-square distribution is continuous, whereas the goodness-of-fit test is
.

Accepted Answer

The answer of The chi-square distribution is continuous, whereas the...

Question 18

A research firm reported that 15% of those surveyed described their health as
poor, 26% as good, 40% as very good, and 19% as excellent. A health
professional in Chicago wanted to determine if people in Chicago had similar
feelings toward their health. In a sample of 610 people in Chicago, 70 described
their health as poor, 180 as good, 220 as very good, and 140 as excellent.
Compute the test value.

Accepted Answer

The answer of A research firm reported that 15% of...

Question 19

$$\text { The null hypothesis should not be rejected for the data given in the figure below. }$$

Accepted Answer

A) True 
 B)False

Question 20

Following are observed frequencies. The null hypothesis is $H _ { 0 } : p _ { 1 } = 0.35 , p _ { 2 } = 0.25$, $p _ { 3 } = 0.1 , p _ { 4 } = 0.1 , p _ { 5 } = 0.2$.
$\begin{array}{l|lllll}
\text { Category } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Observed } & 43 & 20 & 10 & 4 & 31
\end{array}$

Compute the expected frequencies.

Accepted Answer

A)  37.8, 27, 10.8, 10.8, 21.6 
B)  0.398, 0.185, 0.093, 0.037, 0.287 
C)  43, 20, 10, 4, 31 
D)  21.6, 21.6, 21.6, 21.6, 21.6

Exam 11: Other Chi-Square Tests

The computational procedure for the homogeneity of proportions differs from that of the test of independence in that it takes into account the standard deviation.

The formula for finding the chi-square test value is .

The method that uses the formula $\chi ^ { 2 } = \sum \frac { ( | O - E | - 0.5 ) ^ { 2 } } { E }$ is called the________ correction for continuity.

A contingency table has 5 rows and 4 columns. How many degrees of freedom are there?

If the null hypothesis is not rejected, it can be assumed the proportions are 67) and the differences in them are due to chance.

An assumption for the goodness-of-fit test is that the frequency for each category must be five or more.

In a chi-square goodness-of-fit test when there is close agreement between the observed frequency and the expected frequency, the chi-square test value will be small.

The chi-square distribution is continuous, whereas the goodness-of-fit test is .

$\text { The null hypothesis should not be rejected for the data given in the figure below. }$ $\text { The null hypothesis should not be rejected for the data given in the figure below. }$

Exam 11: Other Chi-Square Tests

The computational procedure for the homogeneity of proportions differs from that of the test of independence in that it takes into account the standard deviation.

The formula for finding the chi-square test value is .

The method that uses the formula χ2=∑(∣O−E∣−0.5)2E\chi ^ { 2 } = \sum \frac { ( | O - E | - 0.5 ) ^ { 2 } } { E }χ2=∑E(∣O−E∣−0.5)2​ is called the________ correction for continuity.

A contingency table has 5 rows and 4 columns. How many degrees of freedom are there?

If the null hypothesis is not rejected, it can be assumed the proportions are 67) and the differences in them are due to chance.

An assumption for the goodness-of-fit test is that the frequency for each category must be five or more.

In a chi-square goodness-of-fit test when there is close agreement between the observed frequency and the expected frequency, the chi-square test value will be small.

The chi-square distribution is continuous, whereas the goodness-of-fit test is .

The null hypothesis should not be rejected for the data given in the figure below. \text { The null hypothesis should not be rejected for the data given in the figure below. } The null hypothesis should not be rejected for the data given in the figure below.

The method that uses the formula $\chi ^ { 2 } = \sum \frac { ( | O - E | - 0.5 ) ^ { 2 } } { E }$ is called the________ correction for continuity.

$\text { The null hypothesis should not be rejected for the data given in the figure below. }$ $\text { The null hypothesis should not be rejected for the data given in the figure below. }$