Question 1

Exhibit 7-7: A group of curriculum designers has developed a new system for teaching phonics to young children.They randomly selected 24 kindergarten students to receive either the old phonics method or the new phonics method.The designers realized that kindergartens have morning and afternoon classes, so they wanted to build this factor into the research design.The following is the mean, standard deviation, and number for each group.
$ \begin{array}{lll}\text { Morning } & {\text { Old }}{} & {\text { New }}{} \ & 16.33 & 13.50 \ &1.03 & 2.74 \& 6 & 6 \ \text { Afternoon } & 13.17 & 16.83 \ & 3.55 & 2.14 \ & 6 & 6\end{array} $
The following is an incomplete summary table of the analysis of variance:
 $\begin{array}{ll}
\underline { \text { Source }} & \underline { \text { SS }} & \underline { \text { df }} & \underline { \text {  MS}} & \underline { \text {   F}}\
\text { Time of Day } & 0.042 \
\text { Lesson Design } & 1.042 \
\text { Interaction }\
\text { Error } & 128.500 \
\text { Total } & 102950
\end{array}$
-Refer to Exhibit 7-7.What are the degrees of freedom for Error?

Accepted Answer

The degrees of freedom for Error can be calculated as follows:
df Error = N – (df Time of Day + df Lesson Design + df Interaction)
df Time of Day = 1 (two levels: morning and afternoon)
df Lesson Design = 1 (old vs. new phonics method)
df Interaction = (1)(1) = 1 (product of the two levels)
df Error = 24 – (1+1+1) = 21
Therefore, the correct choice is C.

Question 2

Exhibit 7-10: Choose the appropriate statistic for the following situations.
-Refer to Exhibit 7-10.Is the proportion of people who like Cola A different from the proportion of people who like Cola B?

Accepted Answer

The chi-square test is used to compare the proportions of people who like Cola A and Cola B.

Question 3

Exhibit 7-8: A pet store owner buys equal amounts of supplies for all types of animals.She wonders if the proportions of her customers are equal or are the same.She collected the following data over a period of a week:

$\begin{array}{lccc}
&&& \underline { \text { Products for }}\
&\underline { \text { Dogs }} & \underline { \text { Cats }} & \underline { \text { Fish }} & \underline { \text {  Birds}} & \underline { \text {  Rodents }}\
\text { Customers }&46&48&35&28&28
\end{array}$

-Refer to Exhibit 7-8.The store owner

Accepted Answer

To determine if the proportions of customers per type of animal are equal or not, we need to perform a chi-squared goodness-of-fit test. If the test result indicates a significant difference between the observed values and the expected values (which would be equal if the proportions were indeed equal), then the store owner should adjust the quantity of supplies accordingly. Therefore, more information is needed to perform such test, so option C is not correct. Option A is not necessarily true, as the proportions might not be equal. Therefore, the best choice is B, as the store owner should adjust the quantity of supplies if there is evidence that the proportions of customers are different across animal types.

Question 4

Exhibit 7-9: A group of 100 college students and 100 college graduates was asked to reply to the question, "In general, do you enjoy reading a college textbook?" The following are the results:
 $\begin{array}{llll} 
& \underline{\text {Yes }}{} &\underline{\text {No }}{} &\underline { Sometimes } \
\text { College Students } & 30 & 45 & 25 \
\text { Graduates } & 50 & 30 & 20
\end{array}$
-Refer to Exhibit 7-9.How many degrees of freedom are there for the statistic?

Accepted Answer

The degrees of freedom for a chi-square test of independence are calculated by the formula (r-1)(c-1), where r is the number of rows and c is the number of columns in the table. In this case, there are 2 rows (college students and graduates) and 3 columns (yes, no, sometimes), so the degrees of freedom are (2-1)(3-1) = 2. Therefore, the best choice is B.

Question 5

Exhibit 7-9: A group of 100 college students and 100 college graduates was asked to reply to the question, "In general, do you enjoy reading a college textbook?" The following are the results:
 $\begin{array}{llll} 
& \underline{\text {Yes }}{} &\underline{\text {No }}{} &\underline { Sometimes } \
\text { College Students } & 30 & 45 & 25 \
\text { Graduates } & 50 & 30 & 20
\end{array}$
-Refer to Exhibit 7-9.What is the value for the statistic?

Accepted Answer

To find the value of the statistic, we need to calculate the chi-square test statistic. Using the formula for chi-square, we get:

χ^2 = (30-40)^2/40 + (45-40)^2/40 + (25-20)^2/40 + (50-75)^2/75 + (30-30)^2/30 + (20-20)^2/20

= 2.25 + 0.625 + 0.625 + 6.6667 + 0 + 0

= 10.7667

Using a chi-square distribution table with (2-1)(3-1) = 2 degrees of freedom (df), we find the critical value to be 5.99 at the 5% level of significance. Since our calculated value of χ^2 is greater than the critical value, we reject the null hypothesis and conclude that there is a significant difference in enjoyment of reading college textbooks between college students and college graduates.

Therefore, the value for the statistic is 10.7667, which corresponds to choice (B).

Question 6

Exhibit 7-9: A group of 100 college students and 100 college graduates was asked to reply to the question, "In general, do you enjoy reading a college textbook?" The following are the results:
 $\begin{array}{llll} 
& \underline{\text {Yes }}{} &\underline{\text {No }}{} &\underline { Sometimes } \
\text { College Students } & 30 & 45 & 25 \
\text { Graduates } & 50 & 30 & 20
\end{array}$
-Refer to Exhibit 7-9.The researcher can conclude that

Accepted Answer

The data shows that there are different proportions of students and graduates who enjoy reading a college textbook. Therefore, there is an association between being a student or a graduate and enjoying textbook reading. Option A is not valid because enjoying textbook reading is not necessarily related to the amount of reading done. Option B is not valid because there is evidence to support a conclusion. Option D is not valid because option C is true.

Question 7

Exhibit 7-10: Choose the appropriate statistic for the following situations.
-Refer to Exhibit 7-10.Do first-year college students differ from college seniors on a reading attitude scale?

Accepted Answer

The t-test for independent means is appropriate for comparing two groups on a continuous variable, such as a reading attitude scale, with independent samples, such as first-year college students and college seniors.

Question 8

Exhibit 7-7: A group of curriculum designers has developed a new system for teaching phonics to young children.They randomly selected 24 kindergarten students to receive either the old phonics method or the new phonics method.The designers realized that kindergartens have morning and afternoon classes, so they wanted to build this factor into the research design.The following is the mean, standard deviation, and number for each group.
$ \begin{array}{lll}\text { Morning } & {\text { Old }}{} & {\text { New }}{} \ & 16.33 & 13.50 \ &1.03 & 2.74 \& 6 & 6 \ \text { Afternoon } & 13.17 & 16.83 \ & 3.55 & 2.14 \ & 6 & 6\end{array} $
The following is an incomplete summary table of the analysis of variance:
 $\begin{array}{ll}
\underline { \text { Source }} & \underline { \text { SS }} & \underline { \text { df }} & \underline { \text {  MS}} & \underline { \text {   F}}\
\text { Time of Day } & 0.042 \
\text { Lesson Design } & 1.042 \
\text { Interaction }\
\text { Error } & 128.500 \
\text { Total } & 102950
\end{array}$
-Refer to Exhibit 7-7.Which sources of variance are significant?

Accepted Answer

The answer of Exhibit 7-7: A group of curriculum designers...

Question 9

Exhibit 7-10: Choose the appropriate statistic for the following situations.
-Refer to Exhibit 7-10.The mean grade for an advanced statistics course will be higher than the mean grade for an introductory course in statistics.

Accepted Answer

The appropriate statistic for comparing the means between two independent groups is the t-test for independent means.

Question 10

Exhibit 7-9: A group of 100 college students and 100 college graduates was asked to reply to the question, "In general, do you enjoy reading a college textbook?" The following are the results:
 $\begin{array}{llll} 
& \underline{\text {Yes }}{} &\underline{\text {No }}{} &\underline { Sometimes } \
\text { College Students } & 30 & 45 & 25 \
\text { Graduates } & 50 & 30 & 20
\end{array}$
-Refer to Exhibit 7-9.What is the appropriate statistic for this data?

Accepted Answer

The appropriate statistic for this data is the Chi Square Test of Independence because we want to determine if there is a relationship between the two categorical variables (level of education and enjoyment of reading college textbooks).

Question 11

Exhibit 7-10: Choose the appropriate statistic for the following situations.
-Refer to Exhibit 7-10.A significantly greater proportion of special education teachers have "burned out" compared to the proportion of regular classroom teachers.

Accepted Answer

The appropriate statistic for testing the difference between two proportions is the chi square test.

Question 12

Exhibit 7-7: A group of curriculum designers has developed a new system for teaching phonics to young children.They randomly selected 24 kindergarten students to receive either the old phonics method or the new phonics method.The designers realized that kindergartens have morning and afternoon classes, so they wanted to build this factor into the research design.The following is the mean, standard deviation, and number for each group.
$ \begin{array}{lll}\text { Morning } & {\text { Old }}{} & {\text { New }}{} \ & 16.33 & 13.50 \ &1.03 & 2.74 \& 6 & 6 \ \text { Afternoon } & 13.17 & 16.83 \ & 3.55 & 2.14 \ & 6 & 6\end{array} $
The following is an incomplete summary table of the analysis of variance:
 $\begin{array}{ll}
\underline { \text { Source }} & \underline { \text { SS }} & \underline { \text { df }} & \underline { \text {  MS}} & \underline { \text {   F}}\
\text { Time of Day } & 0.042 \
\text { Lesson Design } & 1.042 \
\text { Interaction }\
\text { Error } & 128.500 \
\text { Total } & 102950
\end{array}$
-Refer to Exhibit 7-7.The designers can conclude

Accepted Answer

The answer of Exhibit 7-7: A group of curriculum designers...

Question 13

Exhibit 7-8: A pet store owner buys equal amounts of supplies for all types of animals.She wonders if the proportions of her customers are equal or are the same.She collected the following data over a period of a week:

$\begin{array}{lccc}
&&& \underline { \text { Products for }}\
&\underline { \text { Dogs }} & \underline { \text { Cats }} & \underline { \text { Fish }} & \underline { \text {  Birds}} & \underline { \text {  Rodents }}\
\text { Customers }&46&48&35&28&28
\end{array}$

-Refer to Exhibit 7-8.What is the appropriate statistic for this question?

Accepted Answer

Chi Square Goodness of Fit is the appropriate statistic because it tests whether the observed distribution of customers across different animal types is significantly different from the expected distribution assuming all animal types have equal proportions of customers.

Question 14

Exhibit 7-10: Choose the appropriate statistic for the following situations.
-Refer to Exhibit 7-10.Do college graduation and generation membership influence the amount of money people are willing to be spend on a house?

Accepted Answer

Multifactor Analysis of Variance is used to analyze the influence of multiple independent variables on a dependent variable. In this case, the independent variables are college graduation and generation membership, and the dependent variable is the amount of money people are willing to spend on a house. A t-test would only compare means between two groups, while a chi-square test is used for categorical data.

Question 15

Exhibit 7-10: Choose the appropriate statistic for the following situations.
-Refer to Exhibit 7-10.The proportion of teachers who take summer courses is greater than the proportion of businesspersons who take summer courses.

Accepted Answer

The answer of Exhibit 7-10: Choose the appropriate statistic for...

Question 16

Exhibit 7-7: A group of curriculum designers has developed a new system for teaching phonics to young children.They randomly selected 24 kindergarten students to receive either the old phonics method or the new phonics method.The designers realized that kindergartens have morning and afternoon classes, so they wanted to build this factor into the research design.The following is the mean, standard deviation, and number for each group.
$ \begin{array}{lll}\text { Morning } & {\text { Old }}{} & {\text { New }}{} \ & 16.33 & 13.50 \ &1.03 & 2.74 \& 6 & 6 \ \text { Afternoon } & 13.17 & 16.83 \ & 3.55 & 2.14 \ & 6 & 6\end{array} $
The following is an incomplete summary table of the analysis of variance:
 $\begin{array}{ll}
\underline { \text { Source }} & \underline { \text { SS }} & \underline { \text { df }} & \underline { \text {  MS}} & \underline { \text {   F}}\
\text { Time of Day } & 0.042 \
\text { Lesson Design } & 1.042 \
\text { Interaction }\
\text { Error } & 128.500 \
\text { Total } & 102950
\end{array}$
-Refer to Exhibit 7-7.What is the F value for the Interaction?

Accepted Answer

To find the F value for the interaction, we need to calculate the interaction sum of squares (SS) and degrees of freedom (df). SS_interaction = SS_total - SS_time of day - SS_lesson design - SS_error = 102.500 - 0.042 - 1.042 - 128.500 = -27.084. However, the sum of squares cannot be negative, so we can conclude that there is no interaction effect. Therefore, the F value for the interaction is 0, and the answer is D (None of these are true).

Question 17

Exhibit 7-8: A pet store owner buys equal amounts of supplies for all types of animals.She wonders if the proportions of her customers are equal or are the same.She collected the following data over a period of a week:

$\begin{array}{lccc}
&&& \underline { \text { Products for }}\
&\underline { \text { Dogs }} & \underline { \text { Cats }} & \underline { \text { Fish }} & \underline { \text {  Birds}} & \underline { \text {  Rodents }}\
\text { Customers }&46&48&35&28&28
\end{array}$

-Refer to Exhibit 7-8.What are the degrees of freedom for the statistic?

Accepted Answer

The degrees of freedom for this statistic would be (number of categories - 1), which in this case is (5-1) = 4. Therefore, the best choice is option C.

Question 18

Exhibit 7-7: A group of curriculum designers has developed a new system for teaching phonics to young children.They randomly selected 24 kindergarten students to receive either the old phonics method or the new phonics method.The designers realized that kindergartens have morning and afternoon classes, so they wanted to build this factor into the research design.The following is the mean, standard deviation, and number for each group.
$ \begin{array}{lll}\text { Morning } & {\text { Old }}{} & {\text { New }}{} \ & 16.33 & 13.50 \ &1.03 & 2.74 \& 6 & 6 \ \text { Afternoon } & 13.17 & 16.83 \ & 3.55 & 2.14 \ & 6 & 6\end{array} $
The following is an incomplete summary table of the analysis of variance:
 $\begin{array}{ll}
\underline { \text { Source }} & \underline { \text { SS }} & \underline { \text { df }} & \underline { \text {  MS}} & \underline { \text {   F}}\
\text { Time of Day } & 0.042 \
\text { Lesson Design } & 1.042 \
\text { Interaction }\
\text { Error } & 128.500 \
\text { Total } & 102950
\end{array}$
-Refer to Exhibit 7-7.Which of the following is associated with greatest power

Accepted Answer

In order to have the greatest power, we want a large effect size, a large number of participants, and small heterogeneity. Choice C has a large effect size, large number, and small heterogeneity, making it the best choice for greatest power.

Question 19

Exhibit 7-8: A pet store owner buys equal amounts of supplies for all types of animals.She wonders if the proportions of her customers are equal or are the same.She collected the following data over a period of a week:

$\begin{array}{lccc}
&&& \underline { \text { Products for }}\
&\underline { \text { Dogs }} & \underline { \text { Cats }} & \underline { \text { Fish }} & \underline { \text {  Birds}} & \underline { \text {  Rodents }}\
\text { Customers }&46&48&35&28&28
\end{array}$

-Refer to Exhibit 7-8.What is the value for the statistic?

Accepted Answer

The value for the statistic is calculated using a chi-square test for goodness of fit. The observed frequencies are compared to the expected frequencies (which are equal if proportions are the same). The calculated chi-square statistic is 9.95.

Question 20

Exhibit 7-10: Choose the appropriate statistic for the following situations.
-Refer to Exhibit 7-10.Do customers spend more through a store's catalog or in person at the store?

Accepted Answer

The answer of Exhibit 7-10: Choose the appropriate statistic for...

Quiz 7: Sampling and Inferential Statistics

Exhibit 7-10: Choose the appropriate statistic for the following situations. -Refer to Exhibit 7-10.Is the proportion of people who like Cola A different from the proportion of people who like Cola B?

Exhibit 7-10: Choose the appropriate statistic for the following situations. -Refer to Exhibit 7-10.Do first-year college students differ from college seniors on a reading attitude scale?

Exhibit 7-10: Choose the appropriate statistic for the following situations. -Refer to Exhibit 7-10.The mean grade for an advanced statistics course will be higher than the mean grade for an introductory course in statistics.

Exhibit 7-10: Choose the appropriate statistic for the following situations. -Refer to Exhibit 7-10.A significantly greater proportion of special education teachers have "burned out" compared to the proportion of regular classroom teachers.

Exhibit 7-10: Choose the appropriate statistic for the following situations. -Refer to Exhibit 7-10.Do college graduation and generation membership influence the amount of money people are willing to be spend on a house?

Exhibit 7-10: Choose the appropriate statistic for the following situations. -Refer to Exhibit 7-10.The proportion of teachers who take summer courses is greater than the proportion of businesspersons who take summer courses.

Exhibit 7-10: Choose the appropriate statistic for the following situations. -Refer to Exhibit 7-10.Do customers spend more through a store's catalog or in person at the store?