Question 1

A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance from the street. A randomly selected sample of 100 property owners was contacted and the results are shown below.  How many degrees of freedom are there?
A) 2
B) 3
C) 4
D) 5

Accepted Answer

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Question 2

To determine if a set of ungrouped, raw data is normally distributed, what test statistic would we use?
A) z-statistic
B) F-statistic
C) Anderson-Darling
D) Chi-square

Accepted Answer

The Anderson-Darling test is a commonly used test for normality that is more powerful than the Shapiro-Wilk test for small to moderate sample sizes. It assesses how well the data fits a normal distribution by comparing the empirical distribution function of the data to the theoretical normal distribution. If the resulting test statistic is small (i.e., the p-value is large), then there is no evidence to reject the null hypothesis that the data is normally distributed.

Question 3

To test for a normal distribution of a frequency distribution with 5 classes, we compute probabilities for each class based on a
A) standard normal distribution.
B) chi-square distribution.
C) student's t distribution.
D) F distribution.

Accepted Answer

To test for a normal distribution of a frequency distribution with 5 classes, we use the normal distribution. The chi-square distribution, student's t distribution, and F distribution are used for testing hypotheses in other situations.

Question 4

A grouped frequency distribution has a mean of 200 and a standard deviation of 20. The class limits for one class are 220 up to 240. What are the standard normal z-statistics for the class limits?
A) -20 and 20.
B) -2.0 and -1.0
C) 200 and 220
D) 1.0 and 2.0

Accepted Answer

The z-statistic is calculated as (X - mean) / standard deviation. For 220: (220-200)/20 = 1.0, and for 240: (240-200)/20 = 2.0.

Question 5

To determine if a set of ungrouped, raw data is normally distributed, the null hypothesis is
A) the data are normally distributed.
B) the data are not normally distributed.
C) the Anderson-Darling test is greater than 0.0.
D) the Anderson-Darling test equal to 0.0.

Accepted Answer

The null hypothesis for testing normality is that the data are normally distributed. Therefore, choice A is the best choice.

Question 6

Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested if exceeding the speed limit was related to social activity. They collected the following responses from 100 randomly selected students:  What is the value of the test statistic?
A) 83.67
B) 9.89
C) 50
D) 4.94

Accepted Answer

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Question 7

A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance from the street. A randomly selected sample of 100 property owners was contacted and the results are shown below.  What is the critical value at the 10% level of significance?
A) 7.779
B) 9.236
C) 9.488
D) 11.070

Accepted Answer

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Question 8

To determine if a set of ungrouped, raw data is normally distributed, we can use
A) Graphical methods.
B) A chi-square test.
C) ANOVA.
D) Regression.

Accepted Answer

Graphical methods, such as a histogram or a normal probability plot, are the most appropriate way to determine if a set of ungrouped, raw data is normally distributed. A chi-square test, ANOVA, and regression are not appropriate for assessing normality of data.

Question 9

A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance from the street. A randomly selected sample of 100 property owners was contacted and the results are shown below.  What is the critical value at the 5% level of significance?
A) 7.779
B) 9.488
C) 9.236
D) 11.070

Accepted Answer

The critical value at the 5% level of significance with 1 degree of freedom (df = n-2) is 9.488 according to the t-distribution table.

Question 10

A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance from the street. A randomly selected sample of 100 property owners was contacted and the results are shown below.  What is the expected frequency for people against the project and who have over 120 feet of property foot-frontage?
A) 1.1
B) 3.9
C) 5.0
D) 5.5

Accepted Answer

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Question 11

A grouped frequency distribution has a mean of 100 and a standard deviation of 20. The class limits for one class are 50 up to 60. Based on the normal distribution, what is the probability that an observation would be in this class?
A) 0.4938
B) 0.4772
C) 0.0166
D) -0.0166

Accepted Answer

The probability is found by calculating the z-scores for the class limits and finding the area under the normal distribution curve between these z-scores. The z-scores are (50-100)/20 = -2.5 and (60-100)/20 = -2. The probability between these z-scores is approximately 0.0166.

Question 12

A grouped frequency distribution has a mean of 200 and a standard deviation of 20. The class limits for one class are 220 up to 240. Based on the normal distribution, what is the probability that an observation would be in this class?
A) 0.1359
B) 0.3413
C) 0.4772
D) 0.8185

Accepted Answer

The z-scores for 220 and 240 are 1 and 2, respectively. The probability between these z-scores is approximately 0.1359.

Question 13

A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance from the street. A randomly selected sample of 100 property owners was contacted and the results are shown below.  What is the expected frequency for people who are undecided about the project and have property front-footage between 45 and 120 feet?
A) 2.2
B) 3.9
C) 5.0
D) 7.7

Accepted Answer

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Question 14

A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance from the street. A randomly selected sample of 100 property owners was contacted and the results are shown below.  What is the expected frequency for people who are in favor of the project and have less than 45 feet of property foot-frontage?
A) 10
B) 12
C) 35
D) 50

Accepted Answer

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Question 15

To test for a normal distribution of a frequency distribution with 5 classes, we need to
A) compute a F-statistic.
B) calculate a t-statistic.
C) convert the class marks to standard normal z-statistics.
D) convert the class limits to standard normal z-statistics.

Accepted Answer

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Question 16

A grouped frequency distribution has a mean of 100 and a standard deviation of 20. The class limits for one class are 50 up to 60. What are the standard normal z-statistics for the class limits?
A) -20 and 20.
B) -2.5 and -2.0
C) 2.0 and 2.5
D) -50 and -40

Accepted Answer

The z-statistic is calculated using the formula z = (X - μ) / σ. For the lower class limit, z = (50 - 100) / 20 = -2.5. For the upper class limit, z = (60 - 100) / 20 = -2.0.

Question 17

To determine if a set of ungrouped, raw data is normally distributed, the cumulative relative frequency distribution of the raw data is compared to a
A) grouped relative frequency distribution.
B) cumulative normal distribution.
C) Anderson-Darling statistic.
D) chi-square statistic.

Accepted Answer

To determine if a set of ungrouped, raw data is normally distributed, the cumulative relative frequency distribution of the raw data should be compared to a cumulative normal distribution. This can be done visually with a normal probability plot or through statistical tests such as the Shapiro-Wilk test or Kolmogorov-Smirnov test. Comparing the data to a grouped relative frequency distribution or using the Anderson-Darling or chi-square statistic would not be appropriate for this purpose.

Question 18

Using a graphical method to determine if a set of ungrouped, raw data is normally distributed, the data would be normally distributed if
A) the plot of the data was curvilinear.
B) the data was randomly distributed.
C) the plot of the data was linear.
D) the plot of the data was significantly different from zero.

Accepted Answer

A graphical method of determining normal distribution involves creating a histogram or a frequency polygon of the data. If the histogram or frequency polygon creates a bell-shaped curve, then the data is normally distributed. Therefore, the plot of the data should be linear, indicating a bell-shaped curve, which corresponds to normal distribution. A curvilinear plot (choice A) suggests non-normality, while a randomly distributed data (choice B) does not sufficiently indicate normality, as the distribution could still be bimodal or skewed. The plot of the data being significantly different from zero (choice D) is not a consideration when determining normality.

Question 19

To test for a normal distribution of a frequency distribution with 5 classes, we need to find
A) the t-statistic.
B) the expected frequency for each class.
C) the class marks.
D) the class relative frequencies.

Accepted Answer

The expected frequency for each class is needed to test for a normal distribution of a frequency distribution with 5 classes.

Question 20

Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested if exceeding the speed limit was related to social activity. They collected the following responses from 100 randomly selected students:  Based on the analysis, what can be concluded?
A) Driving behavior and gender are correlated.
B) Driving behavior and gender are not related.
C) Driving behavior and gender are related.
D) No conclusion is possible.

Accepted Answer

The answer of Recently, students in a marketing research class...

Quiz 17: Nonparametric Methods: Goodness-Of-Fit Tests

To determine if a set of ungrouped, raw data is normally distributed, what test statistic would we use?

To test for a normal distribution of a frequency distribution with 5 classes, we compute probabilities for each class based on a

A grouped frequency distribution has a mean of 200 and a standard deviation of 20. The class limits for one class are 220 up to 240. What are the standard normal z-statistics for the class limits?

To determine if a set of ungrouped, raw data is normally distributed, the null hypothesis is

To determine if a set of ungrouped, raw data is normally distributed, we can use

A grouped frequency distribution has a mean of 100 and a standard deviation of 20. The class limits for one class are 50 up to 60. Based on the normal distribution, what is the probability that an observation would be in this class?

A grouped frequency distribution has a mean of 200 and a standard deviation of 20. The class limits for one class are 220 up to 240. Based on the normal distribution, what is the probability that an observation would be in this class?

To test for a normal distribution of a frequency distribution with 5 classes, we need to

A grouped frequency distribution has a mean of 100 and a standard deviation of 20. The class limits for one class are 50 up to 60. What are the standard normal z-statistics for the class limits?

To determine if a set of ungrouped, raw data is normally distributed, the cumulative relative frequency distribution of the raw data is compared to a

Using a graphical method to determine if a set of ungrouped, raw data is normally distributed, the data would be normally distributed if

To test for a normal distribution of a frequency distribution with 5 classes, we need to find