## CENGAGE | MINDTAP### Complete: Chapter 14 Problem Set#### 1. Identifying Main Effects and InteractionThe results of a two-factor, independent-measures, equal n experiment are summarized in the following matrix. The numerical value in each cell is the mean score obtained from the sample in that treatment condition.Compute the overall means for the scores in \( A_1 \), the scores in \( A_2 \), the scores in \( B_1 \), and the scores in \( B_2 \). Enter each of the means to the right of the appropriate row or below the appropriate column in the matrix.\[\begin{array}{c|c|c|c} & B_1 & B_2 & \\\hlineA_1 & M = 4 & M = 10 & M = \\\hlineA_2 & M = 4 & M = 2 & M = \\\hline & M = & M = & \\\end{array}\]Make a graph of the results of the experiment. Use the blue points (circle symbol) to plot the means for level 1 of factor A (\( A_1 \)). Use the orange points (square symbol) to plot the means for level 2 of factor A (\( A_2 \)). (Note: Line segments will automatically connect your points.)#### Graph ExplanationThe graph displays the experiment's results, plotting the treatment means against the factors. The Y-axis, labeled "Treatment Mean," ranges from 1 to 10. The X-axis is divided into two categories representing the levels of factor B: \( B_1 \) and \( B_2 \).- **Factor A, Level 1 (\( A_1 \))**: Represented by blue circles.- **Factor A, Level 2 (\( A_2 \))**: Represented by orange squares.The plotted points are connected by line segments to visualize the patterns and interactions between the factors.---This text and graph interpretation will help students understand how to analyze and compute result means in a two-factor experiment, and graphically represent those results to observe any interactions between variables. ### Analysis of Two-Way ANOVA Interaction Plot#### Graph Description:The interaction plot provided in the image shows the relationship between two factors, labeled as factor A and factor B, on the treatment mean. The graph is structured as follows:- **X-axis (Horizontal Axis):** - Represents the levels of factor B, which has two levels: Level 1 and Level 2.- **Y-axis (Vertical Axis):** - Represents the Treatment Mean, ranging from 0 to 10.- **Data Points:** - There are two distinct sets of data points corresponding to the two levels of factor A. - **Factor A, level 1:** Represented by blue diamond-shaped markers. - **Factor A, level 2:** Represented by red square-shaped markers.#### Data Interpretation:To determine whether there are main effects for factor A and factor B, and whether there is an interaction between these factors, observe the overall means and the interaction plot.**Main Effect for Factor A:**- Occurs if there is a noticeable difference between the levels of factor A, regardless of the levels of factor B.**Main Effect for Factor B:**- Occurs if there is a noticeable difference between the levels of factor B, regardless of the levels of factor A.**Interaction Effect:**- Occurs if the difference in treatment means between levels of factor A changes depending on the level of factor B.#### Decision Checklist:Based on the provided interaction plot, you need to decide:| | Yes | No ||----------------------|-----|-----|| **Main effect for factor A?** | ( ) | ( ) || **Main effect for factor B?** | ( ) | ( ) || **Interaction?** | ( ) | ( ) |To make these decisions, look for paralleled lines or converging/diverging patterns in the interaction plot. Paralleled lines suggest no interaction, while lines that cross or diverge/converge suggest an interaction.#### Actions:Complete the table by selecting "Yes" or "No" for each question based on your interpretation of the graph.- **Grade It Now:** Submit your answers for immediate feedback.- **Save & Continue:** Save your current answers and continue without submitting.---**Note:** Make sure to review the interaction plot and your understanding of main effects and interaction effects before finalizing your decisions.##### Weather Information:- Temperature:

Since, the number of the question to be solved is not specified, we'll be answering the first…

Answered: 1. Identifying main effects and…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose you were presented with the results of a study comparing two different training methods for basketball athletes. You are told 32 athletes were randomly assigned to the two groups so that 16 were in the group A and 16 were in the group B. At the end of the session, the average scores (wins versus losses) of the two groups/teams were compared and a difference of 10% was observed ( the first team had 10% more wins than the second). The coach observer reports two- sample t-test shows this difference is statistically significant. How would you interpret these findings? What questions or concerns would you have? How might this type of study be improved? Hint: Consider the possibility that the test performed was not the appropriate one.
Julius has conducted a very small study of the amount of sleep his dorm mates get each night. He believes that those who are on one of the school’s sports teams will get more sleep (measured in hours per night) than those who are not. Julius surveyed 12 people. Of these, 6 played on a sports team and 6 did not. The descriptive statistics from his survey are given below. PLAYS SPORTS (Sample 1) DOES NOT PLAY SPORTS (Sample 2) 8 6 9 6 8 5 7 7 8 7 7 6 What is the critical value for this test? what is the t-obtain value for this t-test? Based on your t-obtained value, what should you conclude about the null hypothesis for this test?
The director of student services at Oxnard College is interested in whether women are just as likely to attend orientation as men before they begin their coursework. A random sample of freshmen at Oxnard College were asked what their gender is and whether they attended orientation. The results of the survey are shown below: Data for Gender vs. Orientation Attendance Women Men Yes 440 410 No 238 239 What can be conduded at the a - 0.10 level of significance? For this study, we should use z-test for a population proportion a. The null and alternative hypotheses would be: Ho: Select an answer v Select an answer v Select an answer v (please enter a decimal and note that p1 and ul represent the proportion and mean women and and u2 represent proportion and mean for men.) H: Select an answer v Select an answer v Select an answer v (Please enter a decimal) b. The test statistic ? v (please show your answer to 3 decimal places.) c. The p-value = (Please show your answer to 4 decimal places.) d.…
Acne is a common skin disease that affects most adolescents and can continue into adulthood. A study compared the effectiveness of three acne treatments and a placebo, all in gel form, applied twice daily for 12 weeks. The study's 517 teenage volunteers were randomly assigned to one of the four treatments. Success was assessed as clear or almost clear skin at the end of the 12 week period. The results of the study can be seen in the table below. Using the appropriate statistical test, determine if there is significant evidence that the four treatments perform differently. If so, how do they compare.
You may need to use the appropriate technology to answer this question. A certain manufacturer is a producer of aluminum components for the avionics and automotive industries. At its plant, an engineer has conducted a quality-control test in which aluminum coils produced in all three shifts were inspected. The study was designed to determine if the population proportion of good parts was the same for all three shifts. Sample data follow. Production Shift Quality First Second Third Good 282 364 172 Defective 18 36 28 (1) Using a 0.05 level of significance, conduct a hypothesis test to determine if the population proportion of good parts is the same for all three shifts. State the null and alternative hypotheses. A) H0: p1 = p2 = p3 Ha: Not all population proportions are equal. B) H0: p1 ≠ p2 ≠ p3 Ha: All population proportions are equal. C) H0: At least two population proportions are equal. Ha: p1 ≠ p2 ≠ p3 D) H0: Not all population proportions are equal. Ha: p1 =…
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(OPHTHALMOLOGY) The following data are from a study on Botox injections. Patients received a high-dose injection in one eye (experimental treatment = treatment E) and a low-dose injection in the other eye (control treatment = treatment C). Patients were asked to rate the level of pain in each eye on a 1–10 scale, with higher scores indicating more pain. The assignment of treatments to eyes was randomized. The subjects came back over several visits. Data from the last visit are given in the following table: 1. Which of the following is the correct test to conduct given the situation above? 2. The hypotheses are: 3. What is the level of significance? 4. What is the computed test statistic? Hint: Use (mean of "Pain in E eye") minus (mean of "Pain in C eye") 5. What is the correct decision based on the p-value or critical value method?

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