Type Calories Sodium Standard 153.5539 389.1503 Standard 200.0373 452.4153 Standard 124.8323 524.1963 Standard 171.1112 552.0998 Standard 182.306 420.9485 Standard 145.5536 371.8141 Standard 144.2121 328.5013 Standard 203.5313 433.3854 Standard 129.1697 457.8214 Standard 179.0626 467.4348 Standard 169.7383 469.4691 Standard 137.5783 433.5947 Standard 162.3203 337.1987 Standard 168.9849 409.878 Standard 171.9388 369.1955 Standard 204.5499 296.616 Standard 187.4137 248.7479 Standard 145.0191 319 Standard 193.9999 298 Standard 178.7837 253 Turkey 161.155 432.6506 Turkey 152.5094 426.925 Turkey 157.4322 411.6999 Turkey 146.8106 409.0596 Turkey 148.193 304.8294 Turkey 183.9407 440.5273 Turkey 202.196 632.1959 Turkey 190.8406 346.1161 Turkey 136.7285 373.0043 Turkey 180.9486 445.1544 Turkey 174.7941 432.0749 Turkey 160.966 365.7728 Turkey 119.467 464.7342 Turkey 156.4975 326.6976 Turkey 138.3446 424.6276 Turkey 186.5951 436.1443 Turkey 101.9734 423.7597 Veggie 102.1787 469.4769 Veggie 102.1934 424.8655 Veggie 127.2194 352.1905 Veggie 114.0281 422.0315 Veggie 99.96212 406.1367 Veggie 122.3522 465.8537 Veggie 105.5227 345.6092 Veggie 142.0722 479.4636 Veggie 110.0843 512.7248 Veggie 116.7281 581.1372 Veggie 117.4227 437.0173 Veggie 107.3223 616.3314 Veggie 143.4967 391.8524 Veggie 122.7083 404.3412 Veggie 110.1789 498.7944 Veggie 136.8357 357.6173 Veggie 133.8509 490.2194 Lab Activity 9 One-Way Analysis of Variance (ANOVA) Data Set: Hot Dog One-way analysis of variance is a method for comparing several population means, when the data are from independent samples. It a test that examines the relationship between a quantitative response variable and a categorical explanatory variable, also called factor that has at least three levels or groups. 1. Determining if ANOVA is Appropriate In each part below determine if ANOVA can be used to analyze the scenario. IF ANOVA can be used, write the null and alternative hypotheses. Hint: Since ANOVA is used only in scenarios with a quantitative response variable and categorical explanatory variable (or factor) that has at least three levels, you may find it helpful to first identify the response and explanatory variables and determine if they are categorical or quantitative. a. A psychologist wants to determine if there is a relationship between weather (sunny, partly cloudy, heavy rain, etc.) and mood (happy, carefree, tired, etc.). i. Can ANOVA be used? Explain. IF ANOVA can be used, write the null and alternative hypotheses: ii. Ho: iii. Ha: b. An executive of a national construction company is trying to determine how to be \"low bid\" on more estimates in order to get more jobs. She compares the cost of lumber in dollars in different regions of the United States, specifically, the North, South, East, and West to generate more accurate estimates. i. Can ANOVA be used? Explain. IF ANOVA can be used, write the null and alternative hypotheses: ii. Ho: iii. Ha: c. An HR manager believes that just because employees work long hours does not mean they are productive, agreeing with this article, \"Get a Life,\" from September 24, 2013 in The Economist (http://www.economist.com/blogs/freeexchange/2013/09/working-hours). To test this, the HR manager wants to see if there is a relationship between salary, measured by yearly earnings in dollars, and amount of time worked during the year. i. Can ANOVA be used? Explain. IF ANOVA can be used, write the null and alternative hypotheses: ii. Ho: iii. Ha: d. A nutritionist wants to see if grocery buying habits vary based on level of education. The nutritionist compares the average amount spent in dollars on organic food for three different levels of education: high school diploma, college degree, or advanced degree. i. Can ANOVA be used? Explain. IF ANOVA can be used, write the null and alternative hypotheses: ii. Ho: iii. Ha: e. Given the recent news of Ebola, the US government is trying to keep everyone living in the US at ease. A government official wants to see if their efforts have been successful. He interviews 100 people of various age groups (18-30, 31-45, 45-60, 60-75, 75+) on how worried they are about contracting Ebola on a scale of 1-5, where 1 is not at all worried and 5 is very worried. i. Can ANOVA be used? Explain. IF ANOVA can be used, write the null and alternative hypotheses: ii. Ho: iii. Ha: 2. Exploring ANOVA Visually Below are two dotplots made from random data generated in Minitab. Scenario 1 is on the left and scenario 2 is on the right. The means for data 1, data 2, and data 3 in scenario 1 are all different. Same for scenario 2, the means for data 4, data 5, and data 6 are not equal. Answer the questions below using the dotplots. a. Is it visually easy to detect a difference in means between data 1, data 2, and data 3 in \"scenario 1?\" Explain. b. Is it visually easy to detect a difference in means between data 4, data 5, and data 6 in \"scenario 2?\" Explain. c. Why is a difference in means more clear for \"scenario 2\" than in \"scenario 1?\" 3. One Way ANOVA Using Software Open the Hot Dog data set. This data set contains the calories and sodium content of 54 brands of hot dogs for three different types (beef, turkey, and veggie). A nutritionist wants to determine if there is a health benefit to eating hot dogs that are made from ingredients different from the standard hot dogs. a. Use software to determine the average calorie content for each of the three types of hot dogs. Minitab Express: Statistics > Descriptive Statistics. Enter the variable calories into the \"Variables\" box and enter Type into the \"Group Variable\" box. Standard _______ Turkey _______ Veggie _________ b. Based on the sample means, how do the three types of hot dogs compare in calorie content. Which of the types would the nutritionist recommend? c. The nutritionist wants to determine if the three hot types differ statistically in terms of calorie content. Can the nutritionist use ANOVA for this scenario? Why or why not? d. In words, write the null and alternative hypotheses to test the average calorie content for the three different types of hot dogs. i. Null Hypothesis: ii. Alternative Hypothesis: e. Write the null hypothesis given in part d using appropriate statistical notation. Hint: Remember that ANOVA compares means. And, we have three types of hot dogs. f. Use software to complete a one-way analysis of variance F-test to compare average calorie content of three different types of hot dogs. Copy and paste the output. g. What is the p-value? h. Based on the p-value, make a statistical conclusion. Do we \"fail to reject the null hypothesis\" or \"reject the null hypothesis?\" Explain. i. By rejecting the null hypothesis, we are saying that at least two of the population means differ. But, which one(s)? Using the 95% confidence intervals for the means in the software output, what conclusion is made? Hint: The interval plot shown below from Minitab Express may help visualize the 95% confidence intervals. j. State the real world conclusion. Hint: Think about what the nutritionist would recommend to his or her client. 4. One Way ANOVA - Interpreting Software Output The nutritionist thinks calorie content of the three types of hot dogs is a good start to determining a health benefit between the three hot dog types, but calorie content alone, does not tell the entire health story. As a result, the nutritionist also wants to analyze the sodium content. Use the Minitab Express output to answer the following questions. a. Using the Minitab Express output, write the null hypothesis in statistical notation. Hint: Remember that the DF for the group variable is g-1, where g is the number of groups! b. What is the value of the F-statistic? c. What is the p-value? d. If you did not have a p-value and had only the Tukey Simultaneous 95% confidence interval (CI) output as shown below, what conclusion would you make and why? Be sure to explain your answer! e. Using the p-value, state the statistical conclusion. Should we \"reject the null hypothesis\" or \"fail to reject the null hypothesis?\" Explain. f. g. State the conclusion in \"real world\" terms. Using the results from questions 3 and 4, what type of hot dog would you eat? Why