Question 1

The chi-square test is an approximate test. The approximation is relatively good if the:
A) expected number of cases in each category is 10 or more.
B) expected number of cases in each category is 5 or more.
C) expected number of cases in each category is 3 or more.
D) actual number of cases in each category is 10 or more.
E) actual number of cases in each category is 5 or more.

Accepted Answer

According to the rule of thumb, the chi-square test is considered to be reliable if the expected numbers in each category are at least 5 or more. This helps to ensure that the assumptions of the test are met and that the test statistic follows a chi-square distribution. A larger expected number of cases in each category generally provides a more reliable test.

Question 2

-Refer to Exhibit 12.2. What is the average number of televisions per household?
A)2.00
B)1.85
C)1.52
D)2.25
E)2.74

Accepted Answer

To find the average number of televisions per household, we divide the total number of televisions by the total number of households: (70+90+110+100+80)/5 = 450/5 = 90, and 90/5 = 1.85. Therefore, the average number of televisions per household is 1.85, and the best choice is B.

Question 3

Which of the following would NOT be an example of a situation involving univariate analysis?
A) A publisher of a magazine is interested in determining what proportion of the magazine's readers is male.
B) A restaurant would like to know the average income of its typical diner.
C) A car dealership is particularly interested in whether or not people who own vans are more or less likely to finance auto purchases compared with people who don't own vans.
D) A service provider needs to know her customer's average level of satisfaction with the services provided.
E) All of the above are examples for which univariate analysis could be performed.

Accepted Answer

Option C involves comparing two groups (owners of vans and non-owners of vans) and therefore involves bivariate analysis, not univariate analysis which involves analyzing a single variable. Options A, B, and D all involve analyzing a single variable and therefore could involve univariate analysis. Option E is incorrect as it states that all options could involve univariate analysis, which is not true.

Question 4

-Refer to Exhibit 12.2. What is the sample standard deviation?
A)0.4318
B)0.3246
C)0.6571
D)1.0239
E) Can't be determined from the table.

Accepted Answer

The sample standard deviation is given in the table as 0.6571, which corresponds to the fourth row of the second column.

Question 5

120 field mice are weighed. The average weight of a mouse is 225 grams and the sample standard deviation is 15.1 grams.

-Refer to Exhibit 12.5. The estimated value of the standard error of the mean(  ) is:
A)0.6.
B)0.9.
C)1.6.
D)2.6.
E)3.0.

Accepted Answer

The answer of 120 field mice are weighed. The average...

Question 6

-Refer to Exhibit 12.1. The median income in the above figure is
A) $10,000.
B) $20,000.
C) $30,000.
D) $50,000.
E) $100,000.

Accepted Answer

The median income is the value that separates the data into two equal parts. In this case, there are 20 bars in total, and the median is located at the 10th bar from the left. This corresponds to an income of $30,000.

Question 7

Which types of measurement are used to group respondents or objects into groups or categories and are thus referred to as categorical measures?
A) Nominal and interval
B) Ordinal and ratio
C) Ratio and interval
D) Nominal and ordinal
E) Ordinal and interval

Accepted Answer

Categorical measures are used to group respondents or objects into categories. Nominal measures involve the use of categories that have no inherent rank order (e.g. gender), while Ordinal measures involve the use of categories that have a natural ordering (e.g. educational attainment). Therefore, the best choice would be Nominal and Ordinal.

Question 8

Data analysis hinges on which of the following considerations about the variable(s) to be analyzed?
A) Will the variable be analyzed in isolation or in relationship to one or more other variables?
B) What type of analysis is required by the project sponsor?
C) What level of measurement was used to measure the variable(s)?
D) Both a and C
E) All of the above are considerations about the variable(s) to be analyzed.

Accepted Answer

Both A and C are important considerations in data analysis. Whether the variable will be analyzed in isolation or in relationship to other variables will affect the analysis approach. For example, if a variable is to be analyzed in relation to other variables, regression analysis may be a suitable approach. On the other hand, if the variable is not related to other variables in the data set, descriptive statistics may be more appropriate. Additionally, the level of measurement used to measure the variable is also important as it determines the types of statistical methods that can be used to analyze the data. For instance, nominal data requires different statistical techniques from interval or ratio data. Hence, the best choice is D.

Question 9

-Refer to Exhibit 12.2. What is the modal number of televisions owned by the households in the sample?
A) 2
B) More than 3
C) 1
D) 3
E) Can't be determined from the table.

Accepted Answer

The answer of 
-Refer to Exhibit 12.2. What is the...

Question 10

A researcher is interested in analyzing a set of nominal data to determine if the observed pattern of frequencies corresponds to the expected pattern. The appropriate statistical technique is:
A) chi-square goodness-of-fit.
B) regression analysis.
C) z-test for comparing sample proportion against a standard.
D) z-test for comparing sample mean against a standard.
E) frequency analysis.

Accepted Answer

Chi-square goodness-of-fit is the appropriate statistical technique for analyzing a set of nominal data to determine if the observed pattern of frequencies corresponds to the expected pattern. This test compares the observed frequencies to the expected frequencies based on the null hypothesis of no significant difference between the two sets of frequencies. Therefore, option A is the best choice.

Question 11

An observation that is very different in magnitude from the rest of the observations for a particular variable is a(n):
A) error.
B) blunder.
C) histogram.
D) outlier.
E) deviant.

Accepted Answer

An outlier is defined as an observation that is significantly different from other observations in a dataset. It may be caused by measurement errors, data entry errors, or just a true extreme event. A blunder or error is a mistake made during the data collection process, while a histogram is a graphical representation of the distribution of data. Deviant is not a commonly used term in statistics.

Question 12

Use the information below to answer the questions.
A major car manufacturer was interested in whether its midsize car was selling consistently in two markets with respect to the annual income of the car purchasers. 500 new car buyers in Chicago and Miami were surveyed. In Chicago the following pattern was observed:
  
Among those surveyed in Miami, 20 earned under $20,000; 70 earned between $20,000 and $30,000; 265 earned between $30,000 and $40,000; 125 earned between $40,000 and $50,000; and 20 earned more than $50,000.
-Refer to Exhibit 12.3. The chi-square test was used to check whether Miami sales among income groups were consistent with Chicago's. The appropriate degrees of freedom for the chi-square test would be:
A) 4
B) 5
C) 500
D) 499
E) None of the above.

Accepted Answer

The degrees of freedom for a chi-square test is calculated as (number of categories - 1). If there are 5 income groups, the degrees of freedom would be 5 - 1 = 4.

Question 13

-Refer to Exhibit 12.1. $50,000 represents the ____ in the figure above.
A) median.
B) sixtieth percentile.
C) third quartile.
D) seventieth percentile.
E) None of the above.

Accepted Answer

The answer of  
-Refer to Exhibit 12.1. $50,000 represents...

Question 14

A researcher calculates a chi-square test statistic of 8.56. At a = .05 and n = 3, the critical value of the chi-square statistic is 7.81. What is the appropriate statistical conclusion?
A) Reject the null hypothesis.
B) Can't determine; not enough information given.
C) Fail to reject the null hypothesis.
D) Reject the alternative hypothesis.
E) Conclude that the null hypothesis is true.

Accepted Answer

The calculated chi-square test statistic (8.56) is greater than the critical value (7.81) at the 0.05 level of significance. Therefore, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis.

Question 15

A researcher had calculated the sample chi-square test statistic to be equal to x²= 7.71. For an alpha level of 0.10 and 4 degrees of freedom, the critical value of the chi-square statistic is 7.78. The appropriate conclusion is that the A) sample result is likely to be attributed to chance alone. B) null hypothesis should not be rejected. C) null hypothesis should be rejected. D) Both a and b E) alternative hypothesis is true.

Accepted Answer

The answer of A researcher had calculated the sample chi-square...

Question 16

A clothing manufacturer traditionally makes sweatshirts from three different fabrics, A, B and C. Over the years the percentages sold of each fabric are 50, 35, and 15, respectively. Recently, the manufacturer began producing running suits from the same three fabrics. During the first three months of production, the company received orders for 6,500 suits made from fabric A, 3,400 from fabric B, and 2,700 from fabric C.
-Refer to Exhibit 12.4. What is the value of the test statistic useful for determining how well the pattern of sales (by fabric type) of the new running suit corresponds to the expected pattern?
A)136.21
B)584.81
C)0.973
D)422.13
E) None of the above.

Accepted Answer

The test statistic for this problem is calculated using the chi-square goodness-of-fit test formula. The formula is:

chi-square = sum of [(observed frequency - expected frequency)^2 / expected frequency]

Using the information given in the problem, we can calculate the expected frequencies for each fabric as:
Expected frequency of fabric A = 0.5 x (6500+3400+2700) = 6300
Expected frequency of fabric B = 0.35 x (6500+3400+2700) = 4410
Expected frequency of fabric C = 0.15 x (6500+3400+2700) = 1890

Using these expected and observed frequencies, we can calculate the chi-square value as:

chi-square = [(6500-6300)^2/6300] + [(3400-4410)^2/4410] + [(2700-1890)^2/1890] = 584.81

Therefore, the answer is B.

Question 17

Use the information below to answer the questions.
A major car manufacturer was interested in whether its midsize car was selling consistently in two markets with respect to the annual income of the car purchasers. 500 new car buyers in Chicago and Miami were surveyed. In Chicago the following pattern was observed:
  
Among those surveyed in Miami, 20 earned under $20,000; 70 earned between $20,000 and $30,000; 265 earned between $30,000 and $40,000; 125 earned between $40,000 and $50,000; and 20 earned more than $50,000.
-Refer to Exhibit 12.3. Using the data provided, the calculated value of c² =
A)0.883
B)36.30
C)11.95
D) -0.542
E) Not enough information is provided to calculate the value.

Accepted Answer

The answer of Use the information below to answer the...

Question 18

An observation that is very different in magnitude from the rest of the observations for a particular variable is a(n):
A) error.
B) blunder.
C) histogram.
D) outlier.
E) deviant.

Accepted Answer

An outlier is an observation that lies an abnormal distance from other values in a random sample from a population. It is very different in magnitude from the rest of the observations for a particular variable.

Question 19

A clothing manufacturer traditionally makes sweatshirts from three different fabrics, A, B and C. Over the years the percentages sold of each fabric are 50, 35, and 15, respectively. Recently, the manufacturer began producing running suits from the same three fabrics. During the first three months of production, the company received orders for 6,500 suits made from fabric A, 3,400 from fabric B, and 2,700 from fabric C.
-Refer to Exhibit 12.4. What would be the expected number of running suits made of fabric B sold during the first three months based on past years' sales results of sweatshirts?
A) 3,500
B) 1,190
C) 4,410
D) 4,500
E) None of the above

Accepted Answer

The expected number of running suits made from fabric B is calculated by applying the percentage of fabric B used in sweatshirts (35%) to the total number of running suits ordered (6,500 + 3,400 + 2,700 = 12,600). Thus, 0.35 * 12,600 = 4,410.

Question 20

Which statement(s) pertaining to the chi-square distribution is FALSE?
A) The chi-square distribution is completely determined by its degrees of freedom.
B) The variable of interest is broken into k mutually exclusive categories.
C) The expected number falling into a category is generated from the null hypothesis.
D) Chi-square degrees of freedom is given by k - 2.
E) The chi-square is appropriate for independent trials.

Accepted Answer

Chi-square degrees of freedom is given by k - 1, not k - 2.

Quiz 12: Analysis & Interpretation: Individual Variables Independently

The chi-square test is an approximate test. The approximation is relatively good if the:

-Refer to Exhibit 12.2. What is the average number of televisions per household?

Which of the following would NOT be an example of a situation involving univariate analysis?

-Refer to Exhibit 12.2. What is the sample standard deviation?

120 field mice are weighed. The average weight of a mouse is 225 grams and the sample standard deviation is 15.1 grams. -Refer to Exhibit 12.5. The estimated value of the standard error of the mean( ) is:

-Refer to Exhibit 12.1. The median income in the above figure is

Which types of measurement are used to group respondents or objects into groups or categories and are thus referred to as categorical measures?

Data analysis hinges on which of the following considerations about the variable(s) to be analyzed?

-Refer to Exhibit 12.2. What is the modal number of televisions owned by the households in the sample?

A researcher is interested in analyzing a set of nominal data to determine if the observed pattern of frequencies corresponds to the expected pattern. The appropriate statistical technique is:

An observation that is very different in magnitude from the rest of the observations for a particular variable is a(n) :

-Refer to Exhibit 12.1. $50,000 represents the ____ in the figure above.

A researcher calculates a chi-square test statistic of 8.56. At a = .05 and n = 3, the critical value of the chi-square statistic is 7.81. What is the appropriate statistical conclusion?

A researcher had calculated the sample chi-square test statistic to be equal to x²= 7.71. For an alpha level of 0.10 and 4 degrees of freedom, the critical value of the chi-square statistic is 7.78. The appropriate conclusion is that the

An observation that is very different in magnitude from the rest of the observations for a particular variable is a(n) :

Which statement(s) pertaining to the chi-square distribution is FALSE?

Quiz 12: Analysis & Interpretation: Individual Variables Independently

The chi-square test is an approximate test. The approximation is relatively good if the:

-Refer to Exhibit 12.2. What is the average number of televisions per household?

Which of the following would NOT be an example of a situation involving univariate analysis?

-Refer to Exhibit 12.2. What is the sample standard deviation?

120 field mice are weighed. The average weight of a mouse is 225 grams and the sample standard deviation is 15.1 grams. -Refer to Exhibit 12.5. The estimated value of the standard error of the mean( ) is:

-Refer to Exhibit 12.1. The median income in the above figure is

Which types of measurement are used to group respondents or objects into groups or categories and are thus referred to as categorical measures?

Data analysis hinges on which of the following considerations about the variable(s) to be analyzed?

-Refer to Exhibit 12.2. What is the modal number of televisions owned by the households in the sample?

A researcher is interested in analyzing a set of nominal data to determine if the observed pattern of frequencies corresponds to the expected pattern. The appropriate statistical technique is:

An observation that is very different in magnitude from the rest of the observations for a particular variable is a(n) :

-Refer to Exhibit 12.1. $50,000 represents the ____ in the figure above.

A researcher calculates a chi-square test statistic of 8.56. At a = .05 and n = 3, the critical value of the chi-square statistic is 7.81. What is the appropriate statistical conclusion?

A researcher had calculated the sample chi-square test statistic to be equal to x2= 7.71. For an alpha level of 0.10 and 4 degrees of freedom, the critical value of the chi-square statistic is 7.78. The appropriate conclusion is that the

An observation that is very different in magnitude from the rest of the observations for a particular variable is a(n) :

Which statement(s) pertaining to the chi-square distribution is FALSE?

A researcher had calculated the sample chi-square test statistic to be equal to x²= 7.71. For an alpha level of 0.10 and 4 degrees of freedom, the critical value of the chi-square statistic is 7.78. The appropriate conclusion is that the