Question 1
Exercise 13.11 (Analysis of Variance and the Completely Randomized Design)
How long it takes paint to dry can have an impact on the production capacity of a business. In May , Deal's Auto Body & Paint in Prescott, Arizona, invested in a paint-drying robot to speed up its process (The Daily Courier website, https://www.dcourier.com/photos/2018/may/26/984960336/). An interesting question is, "Do all paint-drying robots have the same drying time?" To test this, suppose we sample five drying times for each of different brands of paint-drying robots. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. The following data were obtained.
Click on the datafile logo to reference the data.
| Robot 1 | Robot 2 | Robot 3 | Robot 4 |
| 128 | 144 | 133 | 150 |
| 137 | 133 | 143 | 142 |
| 135 | 142 | 137 | 135 |
| 124 | 146 | 136 | 140 |
| 141 | 130 | 131 | 153 |
At the level of significance, test to see whether the mean drying time is the same for each brand of robot.
Compute the values identified below (to decimals, if necessary).
| Sum of Squares, Treatment |
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| Sum of Squares, Error |
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| Mean Squares, Treatment |
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| Mean Squares, Error |
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Calculate the value of the test statistic (to decimals).
The -value is
What is your conclusion?
Question 2
Exercise 13.15 Algo (Multiple Comparison Procedures)
To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers, the Jacobs Chemical Company obtained the following data on the time (in minutes) needed to mix the material.
| Manufacturer | ||||
| 1 | 2 | 3 | ||
| 17 | 28 | 23 | ||
| 23 | 26 | 22 | ||
| 21 | 31 | 26 | ||
| 19 | 27 | 25 | ||
a. Use these data to test whether the population mean times for mixing a batch of material differ for the three manufacturers. Use .
Compute the values below (to decimals, if necessary).
| Sum of Squares, Treatment |
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| Sum of Squares, Error |
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| Mean Squares, Treatment |
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| Mean Squares, Error |
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Calculate the value of the test statistic (to decimals).
The -value is
What is your conclusion?
b. At the level of significance, use Fisher's LSD procedure to test for the equality of the means for manufacturers and .
Calculate Fisher's LSD Value (to decimals).
What conclusion can you draw after carrying out this test?
Question 3
In the digital age of marketing, special care must be taken to ensure that programmatic ads appear on websites aligned with a company's strategy, culture, and ethics. For example, in , Nordstrom, Amazon, and Whole Foods each faced boycotts from social media users when automated ads for these companies showed up on the Breitbart website (ChiefMarketer.com website). It is important for marketing professionals to understand a company's values and culture. The following data are from an experiment designed to investigate the perception of corporate ethical values among individuals specializing in marketing (higher scores indicate higher ethical values).
| Marketing Managers | Marketing Research | Advertising |
| 6 | 5 | 6 |
| 5 | 5 | 7 |
| 4 | 4 | 6 |
| 5 | 4 | 5 |
| 6 | 5 | 6 |
| 4 | 4 | 6 |
a. Use to test for a significant difference in perception among the three groups.
Compute the values identified below (to decimals, if necessary).
| Sum of Squares, Treatment |
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| Sum of Squares, Error |
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| Mean Squares, Treatment |
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| Mean Squares, Error |
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Calculate the value of the test statistic (to decimals).
The -value is
What is your conclusion?
b. Using , determine where differences between the mean perception scores occur.
Calculate Fisher's LSD value (to decimals).
Test whether there is a significant difference between the means for marketing managers ( ), marketing research specialists ( ), and advertising specialists ( ).
| Absolute Value | ||
| Difference | (to decimal) | Conclusion |
Question 4
n experiment has been conducted for four treatments with eight blocks. Complete the following analysis of variance table (to decimals but p-value to decimals, if necessary). If answer is zero enter " ".
| Source | Sum | Degrees | Mean | ||
| of Variation | of Squares | of Freedom | Square | -value | |
| Treatments |
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Use to test for any significant differences.
The -value is
What is your conclusion?
Question 5
Are there differences in airfare depending on which travel agency website you utilize? The following data were collected on travel agency websites on July , . The following table contains the prices in U.S. dollars for a one-way ticket between the cities listed on the left for each of the three travel agency websites. Here the pairs of cities are the blocks and the treatments are the different websites.
Click on the datafile logo to reference the data.
| Websites | ||||||
| Flight From ‒ To | Expedia ($) | TripAdvisor ($) | Priceline ($) | |||
| Atlanta to Seattle | 176.00 | 166.00 | 175.80 | |||
| New York to Los Angeles | 195.00 | 195.00 | 206.20 | |||
| Cleveland to Orlando | 77.00 | 72.00 | 76.21 | |||
| Dallas to Indianapolis | 149.00 | 149.00 | 148.20 | |||
Use to test for any significant differences in the mean price of a one-way airline ticket for the three travel agency websites. If your answer is zero, enter " ".
| Source | SS | MS | F | P-value | F crit | |
| of variation | (to decimals) | df | (to decimals) | (to decimals) | (to decimals) | (to decimals) |
| Trip |
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The -value corresponding to Website is
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What is your conclusion?
We the null hypothesis that there is no difference in price among the three websites.
Question 6
A study reported in The Accounting Review examined the separate and joint effects of two levels of time pressure (low and moderate) and three levels of knowledge (naive, declarative, and procedural) on key word selection behavior in tax research. Subjects were given a tax case containing a set of facts, a tax issue, and a key word index consisting of key words. They were asked to select the key words they believed would refer them to a tax authority relevant to resolving the tax case. Prior to the experiment, a group of tax experts determined that the text contained relevant key words. Subjects in the naive group had little or no declarative or procedural knowledge, subjects in the declarative group had significant declarative knowledge but little or no procedural knowledge, and subjects in the procedural group had significant declarative knowledge and procedural knowledge. Declarative knowledge consists of knowledge of both the applicable tax rules and the technical terms used to describe such rules. Procedural knowledge is knowledge of the rules that guide the tax researcher's search for relevant key words. Subjects in the low time pressure situation were told they had minutes to complete the problem, an amount of time which should be "more than adequate" to complete the case; subjects in the moderate time pressure situation were told they would have "only" minutes to complete the case. Suppose subjects were selected for each of the six treatment combinations and the sample means for each treatment combination are as follows (standard deviations are in parentheses).
Excel File: data13-33.xlsx
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| Knowledge | |||
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| Naive | Declarative | Procedural | |
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| Low | 1.13 | 1.56 | 2.00 |
| Time Pressure | ||||
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| Moderate | 0.48 | 1.68 | 2.86 | |
Use the ANOVA procedure to test for any significant differences due to time pressure, knowledge, and interaction. Use a level of significance. Assume that the total sum of squares for this experiment is
Letting Time Pressure be Factor A and Knowledge be Factor B, show the entries in the ANOVA table (to decimals, if necessary). Do not round intermediate calculations. If your answer is zero, enter "0".
| Source of Variation | Sum | Degrees | Mean Square | F | p-value |
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| Factor B |
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The -value for Factor A is
What is your conclusion with respect to Factor A?
The -value for Factor B is
What is your conclusion with respect to Factor B?
The -value for the interaction of factors A and B is
What is your conclusion with respect to the interaction of Factors A and B?
Question 7
A Pew Research study conducted in found that approximately of Americans believe that robots and computers might one day do many of the jobs currently done by people (Pew Research website, http://www.pewinternet.org/2017/10/04/americans-attitudes-toward-a-future-in-which-robots-and-computers-can-do-many-human-jobs/). Suppose we have the following data collected from nurses, tax auditors, and fast-food workers in which a higher score means the person feels his or her job is more likely to be automated.
| Tax | Fast-Food | |
| Nurse | Auditor | Worker |
| 4 | 4 | 5 |
| 5 | 5 | 7 |
| 5 | 4 | 6 |
| 3 | 6 | 4 |
| 3 | 6 | 5 |
| 5 | 5 | 6 |
| 6 | 6 | 5 |
| 5 | 6 | 8 |
a. Use to test for differences in the belief that a person's job is likely to be automated for the three professions.
(to decimals)
The -value is
.
What is your conclusion?
We
the null hypothesis that the mean scores are the same for the three professions.
b. Use Fisher's LSD procedure to compare the belief that a person's job will be automated for nurses and tax auditors.
(to decimals)
What is your conclusion?
We
the null hypothesis that the two population means are equal.
Question 8
A factorial experiment was designed to test for any significant differences in the time needed to perform English to foreign language translations with two computerized language translators. Because the type of language translated was also considered a significant factor, translations were made with both systems for three different languages: Spanish, French, and German. Use the following data for translation time in hours.
| Language | |||
| Spanish | French | German | |
| System 1 | 6 | 14 | 15 |
| 10 | 18 | 19 | |
| System 2 | 10 | 12 | 14 |
| 14 | 14 | 20 | |
Test for any significant differences due to language translator system (Factor A), type of language (Factor B), and interaction. Use .
Complete the following ANOVA table (to decimals, if necessary). Round your p-value to decimal places.
| Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F | p-value |
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The p-value for Factor A is
What is your conclusion with respect to Factor A?
The p-value for Factor B is
What is your conclusion with respect to Factor B?
The p-value for the interaction of factors A and B is
What is your conclusion with respect to the interaction of Factors A and B?
