Concept explainers
A survey of commercial buildings served by the Cincinnati Gas & Electric Company asked what main heating fuel was used and what year the building was constructed. A partial crosstabulation of the findings follows.
Fuel Type | |||||
Year Constructed | Electricity | Natural Gas | Oil | Propane | Other |
1973 or before | 40 | 183 | 12 | 5 | 7 |
1974–1979 | 24 | 26 | 2 | 2 | 0 |
1980–1986 | 37 | 38 | 1 | 0 | 6 |
1987–1991 | 48 | 70 | 2 | 0 | 1 |
- a. Complete the crosstabulation by showing the row totals and column totals.
- b. Show the frequency distributions for year constructed and for fuel type.
- c. Prepare a crosstabulation showing column percentages.
- d. Prepare a crosstabulation showing row percentages.
- e. Comment on the relationship between year constructed and fuel type.
a.
Complete the cross tabulation by showing the row totals and column totals.
Answer to Problem 52SE
The completed cross tabulation is,
Fuel Type | Total | |||||
Year Constructed | Electricity | Natural Gas | Oil | Propane | Other | |
1973 or more | 40 | 183 | 12 | 5 | 7 | 247 |
1974-1979 | 24 | 26 | 2 | 2 | 0 | 54 |
1980-1986 | 37 | 38 | 1 | 0 | 6 | 82 |
1987-1991 | 48 | 70 | 2 | 0 | 1 | 121 |
Total | 149 | 317 | 17 | 7 | 14 | 504 |
Explanation of Solution
Calculation:
The given information is that a partial cross tabulation of fuel type and year constructed.
The row total and column total can be obtained as follows:
The remaining row and column total can be obtained as follows:
Fuel Type | Total | |||||
Year Constructed | Electricity | Natural Gas | Oil | Propane | Other | |
1973 or more | 40 | 183 | 12 | 5 | 7 | 247 |
1974-1979 | 24 | 26 | 2 | 2 | 0 | 54 |
1980-1986 | 37 | 38 | 1 | 0 | 6 | 82 |
1987-1991 | 48 | 70 | 2 | 0 | 1 | 121 |
Total | 149 | 317 | 17 | 7 | 14 | 504 |
b.
Construct a frequency distribution for year constructed and for fuel type.
Answer to Problem 52SE
The frequency distribution for year constructed is,
Year Constructed | Frequency |
1973 or more | 247 |
1974–1979 | 54 |
1980–1986 | 82 |
1987–1991 | 121 |
Total | 504 |
The frequency distribution for fuel type is,
Fuel Type | Frequency |
Electricity | 149 |
Natural Gas | 317 |
Oil | 17 |
Propane | 7 |
Other | 14 |
Total | 504 |
Explanation of Solution
Calculation:
For year constructed:
The frequencies are calculated by using the tally mark for each class interval.
- The class intervals are “1973 or more”, “1974–1979”, “1980–1986” and “1987–1991”.
- Make a tally mark for each value of year constructed in the corresponding class interval and continue for all values in the data.
- The number of tally marks in each class represents the frequency, f of that class.
The frequency distribution for year constructed is obtained as given below:
Year Constructed | Tally marks | Frequency |
1973 or more | 247 | |
1974–1979 | 54 | |
1980–1986 | 82 | |
1987–1991 | 121 | |
Total | 504 |
For fuel type:
Here, “electricity” is the type of fuel which is repeated for 149 times in the data set and thus 149 is the frequency for the fuel type electricity.
Similarly, the frequency of remaining company size is given below:
Fuel Type | Frequency |
Electricity | 149 |
Natural Gas | 317 |
Oil | 17 |
Propane | 7 |
Other | 14 |
Total | 504 |
c.
Compute a cross tabulation showing column percentages for the data.
Answer to Problem 52SE
Cross tabulation of column percentages is:
Fuel Type | |||||
Year Constructed | Electricity | Natural Gas | Oil | Propane | Other |
1973 or more | 26.85 | 57.73 | 70.59 | 71.43 | 50 |
1974–1979 | 16.11 | 8.2 | 11.76 | 28.57 | 0 |
1980–1979 | 24.83 | 11.99 | 5.88 | 0 | 42.86 |
1987–1991 | 32.21 | 22.08 | 11.76 | 0 | 7.14 |
Total | 100 | 100 | 100 | 100 | 100 |
Explanation of Solution
Calculation:
Software procedure:
Step-by-step procedure to construct the column percentage using MINITAB software is given below:
- Choose stat>tables>cross tabulation and chi square.
- Choose raw data (summarized).
- In rows, enter the column of year constructed.
- In columns, enter the column of fuel type.
- Under display, select column percent.
- Click OK
Output using the MINITAB software is given below:
d.
Compute the cross tabulation showing row percentages for the data.
Answer to Problem 52SE
Fuel Type | Total | |||||
Year Constructed | Electricity | Natural Gas | Oil | Propane | Other | |
1973 or more | 16.19 | 74.09 | 4.86 | 2.02 | 2.83 | 100 |
1974–1979 | 44.44 | 48.15 | 3.7 | 3.7 | 0 | 100 |
1980–1979 | 45.12 | 46.34 | 1.22 | 0 | 7.32 | 100 |
1987–1991 | 39.67 | 57.85 | 1.65 | 0 | 0.83 | 100 |
Explanation of Solution
Calculation:
Software procedure:
Step-by-step procedure to construct the row percentage using MINITAB software is given below:
- Choose stat>tables>cross tabulation and chi square.
- Choose raw data (summarized).
- In rows, enter the column of year constructed.
- In columns, enter the column of fuel type.
- Under display, select row percent.
- Click OK
Output using the MINITAB software is given below:
e.
Comment on the relationship between year constructed and fuel type.
Explanation of Solution
Observations from the column percentages cross tabulation:
The percentage of buildings using electricity has not changed greatly over the years. Most of the buildings using natural gas were constructed in 1973 or before. Also for the buildings using oil most of them were constructed in 1973 or before. The percentage of buildings using propane was constructed in 1973 or before.
Observations from the row percentages cross tabulation:
Most of the building was constructed using electricity or natural gas. In 1973 or before most of the buildings used natural gas. In the period 1974–1979, most of the building was constructed using electricity and natural gas. From 1987 onwards most of the building was constructed using natural gas and second largest percentage was constructed using electricity.
Want to see more full solutions like this?
Chapter 2 Solutions
EBK STATISTICS FOR BUSINESS & ECONOMICS
- A college wants to estimate what students typically spend on textbooks. A report fromthe college bookstore observes that textbooks range in price from $22 to $186. Toobtain a 95% confidence level for a confidence interval estimate to plus or minus $10,how many students should the college survey? (We may estimate the populationstandard deviation as (range) ÷ 4.)arrow_forwardIn a study of how students give directions, forty volunteers were given the task ofexplaining to another person how to reach a destination. Researchers measured thefollowing five aspects of the subjects’ direction-giving behavior:• whether a map was available or if directions were given from memory without a map,• the gender of the direction-giver,• the distances given as part of the directions,• the number of times directions such as “north” or “left” were used,• the frequency of errors in directions. Identify each of the variables in this study, and whether each is quantitative orqualitative. For each quantitative variable, state whether it is discrete or continuous. Was this an observational study or an experimental study? Explain your answer.arrow_forwardexplain the difference between the confident interval and the confident level. provide an example to show how to correctly interpret a confidence interval.arrow_forward
- Sketch to scale the orbit of Earth about the sun. Graph Icarus’ orbit on the same set of axesWhile the sun is the center of Earth’s orbit, it is a focus of Icarus’ orbit. There aretwo points of intersection on the graph. Based on the graph, what is the approximate distance between the two points of intersection (in AU)?arrow_forwardThe diameters of ball bearings are distributed normally. The mean diameter is 67 millimeters and the standard deviation is 3 millimeters. Find the probability that the diameter of a selected bearing is greater than 63 millimeters. Round to four decimal places.arrow_forwardSuppose you like to keep a jar of change on your desk. Currently, the jar contains the following: 22 Pennies 27 Dimes 9 Nickels 30 Quarters What is the probability that you reach into the jar and randomly grab a penny and then, without replacement, a dime? Express as a fraction or a decimal number rounded to four decimal places.arrow_forward
- 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
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,