Videos
Below are five questions from a survey of MBA students Answers were written in the blank at the left of each question. For each question, state the data type (categorical, discrete numerical, or continuous numerical) and measurement level (nominal, ordinal, interval, ratio). Explain your reasoning. If there is doubt discuss the alternatives.
a.
Identify the data type as categorical, discrete numerical or continuous numerical and the measurement level as nominal, ordinal, interval or ratio for the given question.
Answer to Problem 35CE
The data type of the question “What is the age of the car you usually drive?” is continuous numerical.
The question has ratio measurement level.
Explanation of Solution
A survey is conducted on MBA students. The given question is, “What is the age of the car you usually drive? (years)”.
Categorical data:
The type of data that naturally take non-numerical values, such as words that can classify or name the data points based on their quality, are called qualitative or categorical data. In order to facilitate the use of statistical methods on categorical data, a commonly used process used is coding, where each value of the categorical variable is coded or represented using a unique number.
Discrete numerical data:
The type of data that can take a countable number of distinct numerical or quantitative values is called a discrete numerical data.
Continuous numerical data:
The type of data that can take an uncountable or infinite number of numerical or quantitative values within any given interval is called a continuous numerical data.
The age of a student’s car can take infinite values within a given interval.
Hence, the data type of the question “What is the age of the car you usually drive?” is continuous numerical.
Nominal measurement:
Nominal measurement is the most basic form of measurement that names or categorizes or classifies data. It is the weakest and easiest form of measurement.
Ordinal measurement:
Ordinal measurement is the measurement that ranks the data in a logical manner. It can be used when a natural ordering is present in the data to give the relative position of one object with respect to another. Numerical values can be assigned to the orders of the data, even when the data values are not naturally numerical. The properties of nominal measurement are applicable for ordinal measurement.
Interval measurement:
Interval measurement is the measurement that can be applied to data that naturally occur in the numerical form and counting of these values is logical. This scale of measurement does not have a meaningful “zero” value. However, the difference between any two points on the scale is meaningful. The operations of addition and subtraction on this scale are meaningful. The properties of nominal and ordinal measurements are applicable for interval measurement.
Ratio measurement:
Ratio measurement is the strongest form of measurement that can be applied to data that naturally occur in the numerical form and counting of these values is logical. This scale of measurement has a meaningful “zero” value. The operations of addition, subtraction, multiplication and division on this scale are meaningful. The properties of nominal, ordinal and interval measurements are applicable for ratio measurement.
The age of a car can be measured. Moreover, the value zero is also logical as the age. The operations of addition, subtraction, multiplication and division can be logically performed on this variable.
Hence, the question “What is the age of the car you usually drive?” has ratio measurement level.
b.
Identify the data type as categorical, discrete numerical or continuous numerical and the measurement level as nominal, ordinal, interval or ratio for the given question.
Answer to Problem 35CE
The data type of the question “About how many times in the past year did you attend formal religious services?” is discrete numerical.
The question has ratio measurement level.
Explanation of Solution
The given variable is, “About how many times in the past year did you attend formal religious services?”
The number of times a student attended a formal religious service in any given year takes distinct numerical values, which are countable in nature. This number cannot take a fractional value.
Hence, the data type of the question “About how many times in the past year did you attend formal religious services?” is discrete numerical.
The number of times a student attended a formal religious service in any given year can be counted. Moreover, the value zero is also logical as the number of services attended by a student. The operations of addition, subtraction, multiplication and division can be logically performed on this variable.
Hence, the question “About how many times in the past year did you attend formal religious services?” has ratio measurement level.
c.
Identify the data type as categorical, discrete numerical or continuous numerical and the measurement level as nominal, ordinal, interval or ratio for the given question.
Answer to Problem 35CE
The data type of the question “How often do you read a daily newspaper?” is categorical.
The question has either ordinal or interval measurement level..
Explanation of Solution
The given variable is, “How often do you read a daily newspaper? (0 = Never, 1 = Occasionally, 2 = Regularly)”
The frequency with which a student reads newspaper is ordered in three categories, which are assigned numerical values. It is not logical to apply mathematical operations to these values.
Hence, the data type of the question “How often do you read a daily newspaper?” is categorical.
The frequency of reading newspaper for a student can be ordered from high to low or from low to high. It can be ranked and assigned numerical values. However, application of mathematical operations is not logical on these values. In this sense, the question “How often do you read a daily newspaper?” has ordinal measurement level.
Likert scale:
The Likert scale is a scale that assigns or codes equidistant values to the ordered categories of a data set. If it is logical to assign such equidistant values to the ordered categories, then an ordinal scale data can be expressed as an interval scale data.
Now, the ordered frequency of reading newspaper for a student can be expressed logically as equidistant values, as on a Likert scale. The operations of addition and subtraction can be logically performed on such variable. However, there is no absolute zero value of these frequencies. One may or may not choose a zero value at their discretion, without any hard-and-fast rule. In this sense, the question “How often do you read a daily newspaper?” has interval measurement level.
d.
Identify the data type as categorical, discrete numerical or continuous numerical and the measurement level as nominal, ordinal, interval or ratio for the given question.
Answer to Problem 35CE
The data type of the question “Can you conduct simple transactions in a language other than English?” is categorical.
The question has nominal measurement level.
Explanation of Solution
The given variable is, “Can you conduct simple transactions in a language other than English? (0 = No, 1 = Yes)”
The ability of a student to conduct simple transactions in a language other than English simply classifies or categorizes the student. It does not take any numerical values naturally.
Hence, the data type of the question “Can you conduct simple transactions in a language other than English?” is categorical.
The ability of a student to conduct simple transactions in a language other than English classifies or categorizes the student. Even when numbers are assigned to such an ability, these cannot be ranked in a logical order. Moreover, it is not logical to perform mathematical operations on such numbers.
Hence, the question “Can you conduct simple transactions in a language other than English?” has nominal measurement level.
e.
Identify the data type as categorical, discrete numerical or continuous numerical and the measurement level as nominal, ordinal, interval or ratio for the given question.
Answer to Problem 35CE
The data type of the question “How often do you exercise (aerobics, running, etc.)?” is categorical.
The question has ordinal measurement level.
Explanation of Solution
The given variable is, “How often do you exercise (aerobics, running, etc.)? (0 = Not at All, 1 = Sometimes, 2 = Regularly)”.
The frequency with which a student exercises is ordered in three categories, which are assigned numerical values. It is not logical to apply mathematical operations to these values.
Hence, the data type of the question “How often do you exercise (aerobics, running, etc.)?” is categorical.
The frequency of exercising of a student can be ordered from high to low or from low to high. It can be ranked and assigned numerical values. However, application of mathematical operations is not logical on these values. In this sense, the question “How often do you exercise (aerobics, running, etc.)?” has ordinal measurement level.
Now, the ordered frequency of exercising of a student can be expressed logically as equidistant values, as on a Likert scale. The operations of addition and subtraction can be logically performed on such variable. However, there is no absolute zero value of these frequencies. One may or may not choose a zero value at their discretion, without any hard-and-fast rule. In this sense, the question “How often do you exercise (aerobics, running, etc.)?” has interval measurement level.
Want to see more full solutions like this?
Chapter 2 Solutions
APPLIED STAT.IN BUS.+ECONOMICS
- A box contains 14 large marbles and 10 small marbles. Each marble is either green or white. 9 of the large marbles are green, and 4 of the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is small or white? Express as a fraction or a decimal number rounded to four decimal places.arrow_forwardCan I get help with this step please? At a shooting range, instructors can determine if a shooter is consistently missing the target because of the gun sight or because of the shooter's ability. If a gun's sight is off, the variance of the distances between the shots and the center of the shot pattern will be small (even if the shots are not in the center of the target). A student claims that it is the sight that is off, not his aim, and wants the instructor to confirm his claim. If a skilled shooter fires a gun at a target multiple times, the distances between the shots and the center of the shot pattern, measured in centimeters (cm), will have a variance of less than 0.33. After the student shoots 28 shots at the target, the instructor calculates that the distances between his shots and the center of the shot pattern, measured in cm, have a variance of 0.25. Does this evidence support the student's claim that the gun's sight is off? Use a 0.025 level of significance. Assume that the…arrow_forwardThe National Academy of Science reported that 38% of research in mathematics is published by US authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 38%. He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 279 recent articles published by reputable mathematics research journals and finds that 123 of these articles have US authors. Does this evidence support the mathematics chairperson's claim that the percentage is no longer 38 % ? Use a 0.02 level of significance. Compute the value of the test statistic. Round to two decimal places.arrow_forward
- A marketing research company desires to know the mean consumption of milk per week among males over age 32. They believe that the milk consumption has a mean of 4 liters, and want to construct a 98% confidence interval with a maximum error of 0.07 liters. Assuming a variance of 0.64 liters, what is the minimum number of males over age 32 they must include in their sample? Round up to the next integer.arrow_forwardSuppose GRE Verbal scores are normally distributed with a mean of 461 and a standard deviation of 118. A university plans to recruit students whose scores are in the top 4 % . What is the minimum score required for recruitment? Round to the nearest whole number, if necessaryarrow_forwardNeed help with my homework thank you random sample of 6 fields of durum wheat has a mean yield of 45.5 bushels per acre and standard deviation of 7.43 bushels per acre. Determine the 80 % confidence interval for the true mean yield. Assume the population is approximately normal. Step 1: Find the critical value that should be used in constructing the confidence interval. Round to three decimal places. Step 2 of 2: Construct the 80% confidence interval. Round to one decimal place. I got 1.476 as my critical value and 41.0 and 49.9 as my confidence intervalarrow_forward
- Can someone check my work? If you draw a card with a value of four or less from a standard deck of cards, I will pay you $14. If not, you pay me $8. (Aces are considered the highest card in the deck.) Step 1 of 2: Find the expected value of the proposition. Round to two decimal places. Losses must be expressed as negative values. PT 2: If you played this game 718 times how much would you expect to win or lose? Round your answer to two decimal places. Losses must be expressed as negative values. for part 1 I got -2.92 pt 2 -2097.56arrow_forwardThe following table describes the distribution of a random sample S of 200 individuals, arranged by education level and income. Income(Dollars per Year) < High School High School Diploma Some College Bachelor’s Degree Graduate Degree Post-Graduate Degree 0-25,000 12 8 3 2 1 0 25,000-50,000 7 12 9 12 11 2 50,000-75,000 1 3 4 6 14 5 75,000-100,000 0 2 1 8 11 8 100,000-125,000 0 1 1 4 8 9 125,000-150,000 0 0 2 3 7 12 150,000+ 0 0 1 1 3 6 Let events be defined as follows: A = the event the subject makes 0-25,000 dollars per yearB = the event the subject makes 25,000-50,000 dollars per year C = the event the subject makes 50,000-75,000 dollars per yearD = the event the subject makes 75,000-100,000 dollars per yearE = the event the subject makes 100,000-125,000 dollars per yearF = the event the subject makes 125,000-150,000 dollars per yearG = the event…arrow_forwardwhat does the central limit theorem, for all samples of the same size n with n>30, the sampling distribution of x can be approximated by a normal distribution mean? What is a real life example using this theoremarrow_forward
- An investigator analyzed the leading digits from 797 checks issued by seven suspect companies. The frequencies were found to be 0, 19, 2, 50, 361, 309, 10, 22, and 24, and those digits correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies are substantially different from the frequencies expected with Benford's law shown below, the check amounts appear to result from fraud. Use a 0.10 significance level to test for goodness-of-fit with Benford's law. Does it appear that the checks are the result of fraud? Leading Digit Actual Frequency Benford's Law: Distribution of Leading Digits 1 2 3 4 5 6 7 8 9 0 19 2 50 361 309 10 22 24 30.1% 17.6% 12.5% 9.7% 7.9% 6.7% 5.8% 5.1% 4.6% Determine the null and alternative hypotheses. Ho The leading digits are from a population that conforms to Benford's law. H₁: At least one leading digit has a frequency that does not conform to Benford's law. Calculate the test statistic, x². x² = (Round to three…arrow_forwardFor the distribution drawn here, identify the mean, median, and mode. Question content area bottom Part 1 A. Aequalsmode, Bequalsmedian, Cequalsmean B. Aequalsmode, Bequalsmean, Cequalsmedian C. Aequalsmedian, Bequalsmode, Cequalsmean D. Aequalsmean, Bequalsmode, Cequalsmedianarrow_forwardA study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? OA. Ho PP2 H₁: P1 P2 OC. Ho H₁₂ H₁: P₁arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning