Concept explainers
Videos
Fill in the given table to identify the characteristics of each variable.
Answer to Problem 26CAP
The table for the characteristics of each variable is,
| Variable |
Qualitative vs Quantitative |
Continuous vs Discrete | Scale of Measurement |
| Sex | Qualitative | Discrete | Nominal |
| Seasons | Qualitative | Discrete | Nominal |
| Time of day | Quantitative | Continuous | Ratio |
| Rating scale score | Quantitative | Discrete | Interval |
|
Movie ratings (1 to 4 stars) | Quantitative | Discrete | Ordinal |
|
Number of students in your class | Quantitative | Discrete | Ratio |
| Temperature (degrees Fahrenheit) | Quantitative | Continuous | Interval |
|
Time (in minutes) to prepare dinner | Quantitative | Continuous | Ratio |
|
Position standing in line | Quantitative | Discrete | Ordinal |
Explanation of Solution
Quantitative variable:
The variable which is measured numerically and it is collected by counting or measuring is termed as quantitative variable. Also, the quantitative variable varies by amount.
Qualitative variable:
The variable which is represented as a label and describes the nonnumeric aspects of phenomena is termed as qualitative variable. Also, the qualitative variable varies by class.
Discrete variable:
If the variable measures whole units or categories that are not distributed along a continuum then it is termed as discrete variable.
Continuous variable:
If the variable measures a long a continuum, that is, it measures at any place beyond the decimal point then it is termed as continuous variable.
Nominal scale:
If measurements in which the numbers are assign to represent something or someone is termed as nominal scale.
Ordinal scale:
The measurements which convey the order or rank alone is said to be ordinal scale.
Interval scale:
The measurements which are distributed in equal units and have no true zero is said to be interval scale. In other words, the interval scale is equidistant but do not have true zero.
Ratio scale:
The measurements which are distributed in equal units and have a true zero is said to be ratio scale. In other words, the interval scale is equidistant and has a true zero. Also, the ratio scale is the most informative scale of measurement.
True zero:
The true zero is nothing on a scale of measurement when the value 0.
For sex:
The variable sex can be represented as labels and it describes nonnumeric aspects of phenomena. Therefore, the variable “sex” is qualitative.
The variable sex (male or female) is finite and it is collected by counting or measuring. Also, it is observed that sex is not a continuous series.
Therefore, the variable “sex” is discrete.
Here, it is observed that the nominal scale converts the sex into number. Therefore, the sex is measured by nominal scale.
For seasons:
The variable seasons (spring, summer, rainy, autumn, fall winter and winter) can be represented as labels and it describes nonnumeric aspects of phenomena. Therefore, the variable “seasons” is qualitative.
The variable ‘seasons’ is finite and it is collected by counting or measuring. Also, it is observed that seasons is not a continuous series.
Therefore, the variable “seasons” is discrete.
Here, it is observed that the nominal scale converts the seasons into number. Therefore, the season is measured by nominal scale.
For time of day:
The variable ‘time of day’ represents the numbers and that can be counted or measured. Thus, the variable time of day is quantitative.
The variable ‘time of day’ would be infinite or it is continuous series because it takes infinitely many values between any two times. Therefore, the variable ‘time of day’ is continuous variable.
Here, it is observed that the time of day is recorded. The time of day distributed in equal parts and it contains a value 0. Therefore, the variable ‘time of day’ is measured by ratio scale.
For rating scale score:
The variable ‘rating scale score’ represents the numbers and that can be counted or measured. Thus, the variable rating scale score is quantitative.
The variable ‘rating scale score’ is finite and it is collected by counting or measuring. Also, it is observed that rating scale score is not a continuous series.
Therefore, the variable “rating scale score” is discrete.
The rating scale score distributed in equal units and it does not true zero. Therefore, the variable rating scale score is measured by interval scale.
For movie rating (one to four stars):
The variable ‘movie rating (one to four stars)’ represents the numbers and that can be counted or measured. Thus, the variable movie rating (one to four stars) is quantitative.
The variable ‘movie rating (one to four stars)’ is finite and it is collected by counting or measuring. Also, it is observed that movie rating (one to four stars) is not a continuous series.
Therefore, the variable “movie rating (one to four stars)” is discrete.
The rating of the movie has a specific order that is based on a 4 star scale. The number 1 may represent ‘not good’, 2 may represent ‘average’, 3 may represent ‘good’ and 4 may represent ‘excellent’. It is clear that the values are arranged with the natural ordering.
Therefore, the variable movie rating (one to four stars) is measured by ordinal scale.
For number of students in a class:
The variable ‘number of students in a class’ represents the numbers and that can be counted or measured. Thus, the variable number of students in a class is quantitative.
The variable ‘number of students in a class’ is finite and it is collected by counting or measuring. Also, it is observed that ‘number of students in a class’ is not a continuous series.
Therefore, the variable ‘number of students in a class’ is discrete.
Here, it is observed that the ‘number of students in a class’ is recorded. The ‘number of students in a class’ distributed in equal parts and it contains a value 0. Therefore, the variable ‘number of students in a class’ is measured by ratio scale.
For temperature (degrees Fahrenheit):
The variable ‘temperature (degrees Fahrenheit)’ represents the numbers and that can be counted or measured. Thus, the variable temperature (degrees Fahrenheit) is quantitative.
The variable ‘temperature (degrees Fahrenheit)’ would be infinite or it is continuous series because it takes infinitely many values between any two degrees Fahrenheit. Therefore, the variable ‘temperature (degrees Fahrenheit)’ is continuous variable.
The temperature (degrees Fahrenheit) distributed in equal units and it does not have true zero. Therefore, the variable temperature (degrees Fahrenheit) is measured by interval scale.
For time (in minutes) to prepare dinner:
The variable ‘time (in minutes) to prepare dinner’ represents the numbers and that can be counted or measured. Thus, the variable time (in minutes) to prepare dinner is quantitative.
The variable ‘time (in minutes) to prepare dinner’ would be infinite or it is continuous series because it takes infinitely many values between any two minutes. Therefore, the variable ‘time (in minutes) to prepare dinner’ is continuous variable.
Here, it is observed that the time (in minutes) to prepare dinner is recorded. The time (in minutes) to prepare dinner distributed in equal parts and it contains a value 0. Therefore, the variable ‘time (in minutes) to prepare dinner’ is measured by ratio scale.
For position standing in line:
The variable ‘position standing in line’ represents the numbers and that can be counted or measured. Thus, the position standing in line is quantitative.
The variable ‘position standing in line’ is finite and it is collected by counting or measuring. Also, it is observed that ‘position standing in line’ is not a continuous series.
Therefore, the variable ‘position standing in line’ is discrete.
The position standing in line has a specific order. That is, the values are arranged with the natural ordering.
Therefore, the position standing in line is measured by ordinal scale.
Hence, the table for the characteristics of each variable is,
| Variable | Qualitative vs. Quantitative | Continuous vs. Discrete | Scale of Measurement |
| Sex | Qualitative | Discrete | Nominal |
| Seasons | Qualitative | Discrete | Nominal |
| Time of day | Quantitative | Continuous | Ratio |
| Rating scale score | Quantitative | Discrete | Interval |
| Movie ratings (1 to 4 stars) | Quantitative | Discrete | Ordinal |
| Number of students in your class | Quantitative | Discrete | Ratio |
| Temperature (degrees Fahrenheit) | Quantitative | Continuous | Interval |
| Time (in minutes) to prepare dinner | Quantitative | Continuous | Ratio |
| Position standing in line | Quantitative | Discrete | Ordinal |
Want to see more full solutions like this?
Chapter 1 Solutions
Statistics for the Behavioral Sciences
- a) Let X and Y be independent random variables both with the same mean µ=0. Define a new random variable W = aX +bY, where a and b are constants. (i) Obtain an expression for E(W).arrow_forwardThe table below shows the estimated effects for a logistic regression model with squamous cell esophageal cancer (Y = 1, yes; Y = 0, no) as the response. Smoking status (S) equals 1 for at least one pack per day and 0 otherwise, alcohol consumption (A) equals the average number of alcohoic drinks consumed per day, and race (R) equals 1 for blacks and 0 for whites. Variable Effect (β) P-value Intercept -7.00 <0.01 Alcohol use 0.10 0.03 Smoking 1.20 <0.01 Race 0.30 0.02 Race × smoking 0.20 0.04 Write-out the prediction equation (i.e., the logistic regression model) when R = 0 and again when R = 1. Find the fitted Y S conditional odds ratio in each case. Next, write-out the logistic regression model when S = 0 and again when S = 1. Find the fitted Y R conditional odds ratio in each case.arrow_forwardThe chi-squared goodness-of-fit test can be used to test if data comes from a specific continuous distribution by binning the data to make it categorical. Using the OpenIntro Statistics county_complete dataset, test the hypothesis that the persons_per_household 2019 values come from a normal distribution with mean and standard deviation equal to that variable's mean and standard deviation. Use signficance level a = 0.01. In your solution you should 1. Formulate the hypotheses 2. Fill in this table Range (-⁰⁰, 2.34] (2.34, 2.81] (2.81, 3.27] (3.27,00) Observed 802 Expected 854.2 The first row has been filled in. That should give you a hint for how to calculate the expected frequencies. Remember that the expected frequencies are calculated under the assumption that the null hypothesis is true. FYI, the bounderies for each range were obtained using JASP's drag-and-drop cut function with 8 levels. Then some of the groups were merged. 3. Check any conditions required by the chi-squared…arrow_forward
- Suppose that you want to estimate the mean monthly gross income of all households in your local community. You decide to estimate this population parameter by calling 150 randomly selected residents and asking each individual to report the household’s monthly income. Assume that you use the local phone directory as the frame in selecting the households to be included in your sample. What are some possible sources of error that might arise in your effort to estimate the population mean?arrow_forwardFor the distribution shown, match the letter to the measure of central tendency. A B C C Drag each of the letters into the appropriate measure of central tendency. Mean C Median A Mode Barrow_forwardA physician who has a group of 38 female patients aged 18 to 24 on a special diet wishes to estimate the effect of the diet on total serum cholesterol. For this group, their average serum cholesterol is 188.4 (measured in mg/100mL). Suppose that the total serum cholesterol measurements are normally distributed with standard deviation of 40.7. (a) Find a 95% confidence interval of the mean serum cholesterol of patients on the special diet.arrow_forward
- The accompanying data represent the weights (in grams) of a simple random sample of 10 M&M plain candies. Determine the shape of the distribution of weights of M&Ms by drawing a frequency histogram. Find the mean and median. Which measure of central tendency better describes the weight of a plain M&M? Click the icon to view the candy weight data. Draw a frequency histogram. Choose the correct graph below. ○ A. ○ C. Frequency Weight of Plain M and Ms 0.78 0.84 Frequency OONAG 0.78 B. 0.9 0.96 Weight (grams) Weight of Plain M and Ms 0.84 0.9 0.96 Weight (grams) ○ D. Candy Weights 0.85 0.79 0.85 0.89 0.94 0.86 0.91 0.86 0.87 0.87 - Frequency ☑ Frequency 67200 0.78 → Weight of Plain M and Ms 0.9 0.96 0.84 Weight (grams) Weight of Plain M and Ms 0.78 0.84 Weight (grams) 0.9 0.96 →arrow_forwardThe acidity or alkalinity of a solution is measured using pH. A pH less than 7 is acidic; a pH greater than 7 is alkaline. The accompanying data represent the pH in samples of bottled water and tap water. Complete parts (a) and (b). Click the icon to view the data table. (a) Determine the mean, median, and mode pH for each type of water. Comment on the differences between the two water types. Select the correct choice below and fill in any answer boxes in your choice. A. For tap water, the mean pH is (Round to three decimal places as needed.) B. The mean does not exist. Data table Тар 7.64 7.45 7.45 7.10 7.46 7.50 7.68 7.69 7.56 7.46 7.52 7.46 5.15 5.09 5.31 5.20 4.78 5.23 Bottled 5.52 5.31 5.13 5.31 5.21 5.24 - ☑arrow_forwardく Chapter 5-Section 1 Homework X MindTap - Cengage Learning x + C webassign.net/web/Student/Assignment-Responses/submit?pos=3&dep=36701632&tags=autosave #question3874894_3 M Gmail 品 YouTube Maps 5. [-/20 Points] DETAILS MY NOTES BBUNDERSTAT12 5.1.020. ☆ B Verify it's you Finish update: All Bookmarks PRACTICE ANOTHER A computer repair shop has two work centers. The first center examines the computer to see what is wrong, and the second center repairs the computer. Let x₁ and x2 be random variables representing the lengths of time in minutes to examine a computer (✗₁) and to repair a computer (x2). Assume x and x, are independent random variables. Long-term history has shown the following times. 01 Examine computer, x₁₁ = 29.6 minutes; σ₁ = 8.1 minutes Repair computer, X2: μ₂ = 92.5 minutes; σ2 = 14.5 minutes (a) Let W = x₁ + x2 be a random variable representing the total time to examine and repair the computer. Compute the mean, variance, and standard deviation of W. (Round your answers…arrow_forward
- The acidity or alkalinity of a solution is measured using pH. A pH less than 7 is acidic; a pH greater than 7 is alkaline. The accompanying data represent the pH in samples of bottled water and tap water. Complete parts (a) and (b). Click the icon to view the data table. (a) Determine the mean, median, and mode pH for each type of water. Comment on the differences between the two water types. Select the correct choice below and fill in any answer boxes in your choice. A. For tap water, the mean pH is (Round to three decimal places as needed.) B. The mean does not exist. Data table Тар Bottled 7.64 7.45 7.46 7.50 7.68 7.45 7.10 7.56 7.46 7.52 5.15 5.09 5.31 5.20 4.78 5.52 5.31 5.13 5.31 5.21 7.69 7.46 5.23 5.24 Print Done - ☑arrow_forwardThe median for the given set of six ordered data values is 29.5. 9 12 23 41 49 What is the missing value? The missing value is ☐.arrow_forwardFind the population mean or sample mean as indicated. Sample: 22, 18, 9, 6, 15 □ Select the correct choice below and fill in the answer box to complete your choice. O A. x= B. μεarrow_forward
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,