STAT200 Lesson 10: One-Way ANOVA Lab Assignment complete solutions correct answers key

STAT200 Lesson 10: One-Way ANOVA Lab Assignment complete solutions correct answers key

Answer the following questions showing all work. For questions that require Minitab Express, include the appropriate output (copy + paste) along with an explanation. For all tests use an alpha level of .05 unless otherwise specified.

1.For each of the following scenarios, would a one-way analysis of variance be the most appropriate statistical procedure?  Explain why or why not. (10 points)

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.    The marketing team for a nation-wide travel agency wants to know if adults with high school, associates, bachelors, masters, and doctoral degrees differ in terms of the amount of money they spend on travel annually.

IF ANOVA can be used, write the null and alternative hypotheses:

i.  Ho:

ii.  Ha:

B.     A bakery wants to know if men, women, and children differ in terms of whether or not they like red velvet cupcakes.

IF ANOVA can be used, write the null and alternative hypotheses:

i.  Ho:

ii.  Ha:

C.    Medical researchers want to compare the effectiveness of a calcium supplement, a vitamin d supplement, a calcium + vitamin d supplement, and a placebo pill at preventing osteoporosis in women in their early 80s. They obtain a sample of 100 women who are 80 years old. The women are randomly assigned to receive one of the four treatments.  After 5 years the researchers record the proportion of women in each treatment group who have been diagnosed with osteoporosis.

IF ANOVA can be used, write the null and alternative hypotheses:

i.  Ho:

ii.  Ha:

D.    An educational researcher wants to compare the effectiveness of three different instructional methods. Students are randomly assigned to receive one of the three instructional methods.  After four weeks of instruction their knowledge is measured using an exam worth up to 100 points.

IF ANOVA can be used, write the null and alternative hypotheses:

i.  Ho:

ii.  Ha:

E.     A group of researchers have measured the wrist diameter, wrist flexibility, and body mass index of 50 adult males. They want to examine the relationships between the three variables.

IF ANOVA can be used, write the null and alternative hypotheses:

i.  Ho:

ii.  Ha:

2.    (3 points)

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.

determine if there is evidence that the mean number of calories is different 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. 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. (12 points—part E worth 5 points, part F worth 2 points)

A.      Use software to determine the average calorie content for each of the three types of hot dogs.

●     Minitab:  Stat > Basic Statistics > Display Descriptive Statistics. Enter the variable calories in the Variables box and enter type in the “By Variables” box.

●     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. Has the assumption of equal variances been met?  Explain how you checked for this.

 E.  Use the five-step hypothesis testing procedure to for the three types of hot dogs.

 Write out all five steps! (worth 5 points)

F. Make all possible pairwise comparisons using Tukey’s Honestly Significant Differences Test.  Which if any pairs are different?  Copy and Paste Output.   (worth 2 points)

G. How would you explain these results to a friend who has no knowledge of statistics?

4. Open the dataset STARS.MTW. This file contains data from three different sections of an introductory statistics course from Fall 2015. The students in those courses completed the statistics anxiety rating scale (STARS) at the beginning of one semester. (8 points--part A is worth 5 points, part B is worth 2 points)

A. Use the five-step hypothesis testing procedure to determine if there is evidence of a difference in the STARS scores of students in the three sections of the course. Write out all five steps!  (worth 5 points)

B. Make all possible pairwise comparisons using Tukey’s Honestly Significant Differences Test.  Which pairs are different?  Copy and Paste Output. (worth 2 points)

C. How would you summarize your results from parts A and B for a statistician?

4.  A research study was performed to examine the average body mass index (BMI) of adult men from three different countries. In the study, 40 individuals from each country were randomly selected.  Use the information given to answer the following questions. (15 points—part A worth 14 points)

Source

SS

df

MS

F

p

Between Groups

62.486

Within Groups

713.291

Total

775.777

A. Fill in all of the blank cells in the ANOVA source table above.             (worth 12 points)

B. Is there evidence to state that the mean BMIs of men from these three countries are not all equal? Explain how you came to this conclusion.