LESSON Lesson Objectives:  Student will write null and alternative hypotheses.Student will find critical values for testing a mean or proportion against the population mean or proportion using the appropriate test, based on the sample size.Student will find critical values for testing the difference between two means or two proportions using the appropriate test, based on the sample size. What is a hypothesis?In science, you may have learned that the hypothesis is an educated guess.  In statistics, the same definition carries over but has some different applications.  A statistical study is similar to the scientific method.  From science you have learned that the scientific method includes the following steps:  1) Ask a question 2) Do background research 3) Construct a hypothesis 4) Test your hypothesis by doing an experiment 5) Analyze the data and draw a conclusion 6) Communicate the results.  In statistics, there are two hypotheses that need to be formed once you have defined the problem and completed background research.  One is called the ‘null’ hypothesis and the other is called the ‘alternative’ hypothesis.  Once the study is conducted, we can reject or fail to reject either of the hypothesis based on the results of the study.The Null HypothesisThe null hypothesis is composed of the fact that there is no effect of the treatment on the subjects in the study.  For example if we were trying to investigate the relationship between two variables our null hypothesis may state that ‘there is no relationship between the two variables’ or if we are trying to see if a new drug has an effect on weight gain the null hypothesis may state that ‘the drug has no effect on the weight gain of the subjects’.  The null hypothesis is the one that we will fail to reject (accept) unless the data provides convincing evidence that it is false.The Alternative HypothesisThe alternative hypothesis may be referred to as the opposite of the null hypothesis.  For example, if the null hypothesis states that there is no relationship between two variables, then the alternative hypothesis should state that ‘there is a relationship between the two variables that can be measured.  If the null hypothesis states that there is no effect on the subject then the alternative hypothesis should state that ‘there is an effect on the subject’.  We will fail to reject (accept) the alternative hypothesis if and only if the data provides convincing evidence that it is true.  Practice Writing Null and Alternative HypothesesThe hypotheses can be written out in words or we may use mathematical symbols to express the hypothesis.  Here a few examples of how to write the null and alternative hypothesis.  The most common symbol for the null hypothesis is H0 and the most common symbol for the alternative hypothesis is H1.Let’s Practice:   Case I: An agriculturist is doing a study to determine if a fertilizer has any effect on the average height of 100 apple trees.  He knows that the average height of unfertilized apple trees is 10ft.  The average height of the 100 apple trees that were treated with fertilizer is 10.8 feet with a standard deviation of .5 ft.  1)  Do you think that the fertilizer has an effect on the height of the apple trees?H0 = The fertilizer has no effect on the height of the apple trees                         Sample mean = Population meanH1 = The fertilizer does have an effect on the height of the apple trees.             Sample mean  ≠ Population mean2)  Does the fertilizer make the apple trees taller?H0 = The fertilizer does not make the apple trees taller.                                     Sample mean = Population meanH1 = The fertilizer does make the apple trees taller.                                           Sample mean > Population meanRemember that when writing and testing hypotheses it is very important that you consider the question that want to answer with your study because this fact helps to shape the correct hypotheses.Choosing the Appropriate TestChoosing the appropriate test for any statistical research is very important to obtaining the most accurate results.  We discussed in a previous lesson when to use a z-score or z-test and when to use a t-score or a t-test.  Recall that we use a z-test when the sample size is fairly large (greater than 100) and a t-test when the sample size is small (less than 100).  Another question that we need to consider is when to use a two- tailed test or a one- tailed test.  This choice is made based upon the statement of the alternative hypothesis.  We would use a two-tailed test if our alternative hypothesis is the exact opposite of the null hypothesis.  We would use a one-tailed test if our alternative hypothesis suggests a certain direction for the results.  If  H0 = There is no effect on the variable , then H1 = There is an effect on the variable.In this case we would use a two tailed test.If H0 = The mean sample mean is equal to the population mean , then H1 = The sample mean is greater than the population mean.In this case we would use the one-tailed test since we are concerned with only the right side of the probability distribution where the values are that are greater than the mean.Click here for a video explaining when to use a one-tailed test and when to use a two tailed test.Critical Values & Testing a HypothesisTesting a hypothesis includes finding the appropriate z or t score and finding critical values to compare it to the probability of an event and its position on the normal distribution curve given a confidence interval or p-value.  A critical value is the value of the dependent variable at a given point of a function that helps us to decide to reject or fail to reject the null hypothesis.  If the test statistic is this number or more then we will reject the null hypothesis but if the test statistic is less than this number then we will fail to reject or accept the null hypothesis.  Consider these examples:Testing the mean against the population mean  An agriculturist is doing a study to determine if a fertilizer has any effect on the average height of 100 apple trees.  He knows that the average height of unfertilized apple trees is 10ft.  The average height of the 100 apple trees that were treated with fertilizer is 10.1 feet with a standard deviation of 0.5 ft.  Do you think that the fertilizer has an effect on the height of the apple trees?Step 1:  Write the null and alternative hypothesesH0 = The fertilizer has no effect on the height of the apple trees                         Sample mean = Population meanH1 = The fertilizer does have an effect on the height of the apple trees.             Sample mean  ≠ Population meanStep 2:  We will assume that the null hypothesis is true and find the z-score (since we have a large sample).  z = 10 – 10.1/(.5/√100) = -2  Step 3:  Find the critical value by applying the subtracting (since the z-score is negative) the product of the z-score and the standard deviation from the population mean.10 – 2(.5) = 9 so the critical value is 9Since the mean of the sample is greater than this critical value we must reject the null hypothesis.Testing a proportion against the population proportionA company found that in a sample of 100 of its products that 25 were defective after retraining the employees.  If there is an overall 60% chance that the company will produce a defective product, did the training help employees minimize the number of defective products?Step 1:  Write the null and alternative hypothesis.H0 = p = 60% or .6        The training had no effect on the proportion of defective productsH1 = p < 60% or .6        The training helped to decrease the proportion of defective products.Remember that these types of problems are binomial experiments so we have to be sure that we can use the normal approximation by confirming that (n)(p) and (n)(q) are both greater than 5.  So (100)(.6) = 60 and (100)(.4) = 40, we may proceed.Step 2:  Assume that the null hypothesis is true and find the standard deviation ( standard deviation = √(n)(p(q)) so that we can find the z-score.standard deviation = 4.33z = .25 – .6/ 4.33 = -.08Step 3:  Find the critical value by subtracting (since the z-score is negative) the product of the z-score and the standard deviation from the mean..6 – .3464 = .2536 or 25.36 %  since our test statistic is .6 or 60% and it is more than the critical value then we must reject the null hypothesis and conclude that training did decrease the number of defective products.Testing the Difference of Means and Difference of ProportionsThe difference of means or difference of proportions is used to find out whether there is a significance between the controlled group and the uncontrolled group.  We can also use critical values to determine the significance for the difference of means as well as the difference of proportions.Difference of Means:A teacher gave 100 students a study guide in preparation for a major test.  The average score for these students was 88 with standard deviation of 2.  She did not give study guides to another group of 100 students and the average score for these students was 80 with a standard deviation of 3.  Determine whether the study guide had an effect on student scores.Step 1:  Find the difference in the sample mean scores.  88-80 = 8 Step 2:  Write the null and alternative hypotheses.H0 = The study guide has no effect on student test scores or population mean1 = population mean2 or population mean1 – population mean2 = 0 H1 = The study guide has an effect on student test scores or population mean1 ≠ population mean2 or population mean1 – population mean2 ≠ 0Step 3:  Calculate the standard deviation for the difference of the sample means.  To do this we need to find the variance (square the standard deviation for each sample) and divide it by n for each sample then add the two values together and take the square root.√[(22 )/100 + (32 )/100] = √4/100 + 3/100 = √7/100 = √.07 = .26Step 4:  Assume that the null hypothesis is true and find the z-score using the difference of the means.z = 0-8/.26 = -30.76  find the critical value by adding (since the z-score is positive) the product of the z-score and the standard deviation to the test statistic.  0 – 8 = -8 This is the critical value and since the test statistic 0 is must than this value we must reject the null hypothesis and conclude that the study guide has an effect on student test scores.NEXT TEACHER OFFICE HOURS ARE: Grading Rubric: Grading for this lesson:To get a 10: All answers are correct the first time, or within first revision. To get a 9: You can have 1 incorrect answer after your original submission.To get an 8: You can have 2 incorrect answers after your original submission.To get a 7: You can have 3  incorrect answers after your original submission. To get a 6: You can have 4 incorrect answers after your original submission.To get a 5: Cheating- Plagiarism – purposeful or mistaken, which will lower your final grade for the course (so be very careful when posting your work!); lack of effort, disrespect, or attitude (we are here to communicate with you if you don't understand something); lesson requirements have not been met. Note:  For this class it is necessary to post the questions over each answer. Failure to do so will result in asking for a revision.   No grade will be given for incomplete work. Assignment:For questions 1-5, write the null and alternative hypothesis.1.  Does the water temperature have an effect on the number of people in the pool?2.  Does the weather have an effect on the number of people at the beach?3.  A fitness center is running a discounted membership fee.  Did the discount increase the membership sales? Write your hypotheses mathematically.4.  A medical researcher gave 100 patients a new drug to see if it reduces their blood pressure?  Did the new drug reduce the patients' blood pressure?  Write your hypothesis mathematically.5.  Some students took a conflict resolution class?  Did this class help to reduce the number of conflicts that the students were involved in?  Write your hypothesis mathematically.For questions 6-10, find the critical value.6.  There is an annual hot dog eating contest in Plattsburg, MS and the average number of hot dogs eaten by one person is 36 with a standard deviation of 6.  Find the critical value for a person who can eat more than 2 deviations above the mean.7.  Female high school seniors at a particular school have an average height of 65 inches with a standard deviation of 5 inches.  Find the critical value for a female high senior who is less than 1 deviation from the mean.8.  The average weight of a newborn at a particular hospital is 96 ounces with a standard deviation of 3 ounces.  Find the critical value for a newborn who is 2 standard deviations below the average weight.9.  A company found that 27 out of 150 of its products were defective after retraining its employees.  If the company normally has a 40% defective product rate, find the critical value to determine if retraining the employees helped to minimize the number of defective products.10.  A teacher gives 200 students a study guide for a test and the average score was 90 with a standard deviation of 6.  She did not give the other 200 students a study guide and their average score was 70 with a standard deviation of 8.  Find the critical value to determine whether or not the study guide helped students to increase their test score.

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Ashford 6: – Week 5 – Final PaperLetter of AdviceFor this assignment, you will write a letter of advice to either a newly engaged couple or a group of coworkers. Imagine that either the engaged couple or coworkers hear that you are taking a course in interpersonal communication and want advice regarding how to communicate in their personal or professional relationships. Based on what you have learned in this course, your personal experience, and the five learning objectives we have covered, what advice would you give them regarding how to communicate effectively? How can you use what you have learned in this class to offer a couple or group of co-workers advice to have more positive relationships? Write your paper in the form of a letter. Please review the Sample Final Paper.InstructionsUse the list of learning outcomes to write your letter. The course learning outcomes you will need to cover are listed below:Explain the principles of and barriers to effective interpersonal communications.Analyze the role of communication in developing and maintaining one’s self-concept, self-image, and self-esteem.Differentiate appropriate levels of self-disclosure and emotional intelligence in various relationships.Describe strategies for using communication techniques to resolve interpersonal conflicts.Analyze the impact of gender and culture on interpersonal communications.For each of the five learning outcomes, create a separate heading that states the learning outcome that you are addressing. Then, address the following for each segment:Explain the principles of and barriers to effective interpersonal communications. Why do the principles matter? How can your couple or group of co-workers overcome the barriers you have listed?Analyze the role of communication in developing and maintaining one’s self-concept, self-image, and self-esteem. Begin by defining each term and then explain how these three notions of the self potentially impact the relationships of your couple or group of co-workers. What advice can you offer to help them develop a positive self-concept or build each other’s self-esteem?Illustrate the importance of self-disclosure and emotional intelligence in various relationships. What role does self-disclosure play in the relationships of your couple or co-workers? How can their relationships be improved by them becoming more emotionally intelligent? What connections can be made between emotional intelligence and self-disclosure?Evaluate strategies for using communication techniques to resolve interpersonal conflicts. Explain one or two potential conflicts and then present at least two strategies for addressing the dispute(s).Analyze the impact of gender and culture on interpersonal communications. First, define these two key terms. Then, explain the importance of gender and culture in relationships generally and for your couple or group of co-workers specifically. What advice can you give to become a better communicator based on the information you have presented?Content RequirementsYou must address all five of the learning outcomes and the questions listed with those objectives. For each objective, be sure to define key terms and relate those ideas directly to advice for your couple or co-workers. The point here is for you to demonstrate how these ideas can be utilized to help people in their relationships. Try to offer specific advice they can integrate into their lives.Begin your paper with an introductory paragraph that has a succinct thesis statement and that previews what you plan to cover in your paper. End with a conclusion that reaffirms your thesis and restates your key points.You must use at least five scholarly sources to help you make your points. At least three of these should be course readings and two should be academic articles you have found yourself by doing research in the Ashford University Library. If you need help doing research, visit the Ashford University Library, which can be accessed through the Library tab in the left-navigation menu, in your online course.You must also draw on personal experience to offer advice or to illustrate points. It is acceptable to use hypothetical examples and/or your personal experiences for either your couple or group of co-workers. We simply want to see that you can apply what you have learned to some potential “real world” experience.The Final PaperMust be 8 to 10 double-spaced pages in length (not including title and references pages) and formatted according to APA style. For assistance, visit the Ashford Writing Center’s APA Essay Checklist for Students.Must include a title page with the following: (For further assistance with the formatting and the title page, please refer to the Formatting Instructions for MS Word 2013)Title of paperStudent’s nameCourse name and numberInstructor’s nameDate submittedMust include an introduction and conclusion paragraph. Your introduction paragraph needs to end with a clear thesis statement that indicates the purpose of your paper. For assistance on writing Introductions and Conclusions as well as Thesis Statements, please refer to the Ashford Writing Center resources.Must use each learning objectives as a header dividing each section of the paper.Must use the textbook as a source. The Integrating Research tutorial will offer further assistance on including supporting information and reasoning.Must use two additional course articles/videos and two academic articles the student has found independently. A total of five sources must be used in the paper and be on the reference list.Must document any information from a source in APA style, as outlined in the Ashford Writing Center’s In-Text Citation Guide.Must include a separate APA References List that is formatted according to APA style.Before you submit your written assignment, you are encouraged to review The Grammarly Guide: How to Set Up & Use Grammarly tutorial, set up a Grammarly account (if you have not already done so), and use Grammarly to review a rough draft of your assignment. Then carefully review all issues identified by Grammarly and revise your work as needed.Final NotesThis is a formal paper and should utilize proper grammar, complete sentences, and paragraph transitions. However, you will write this paper in the format of a letter to the newly-engaged couple or group of co-workers. Feel free to address the people you select directly throughout the paper.After you have written the paper, please review the grading rubric to ensure you have met all of the requirements.Need more help?In this class, you have three tutoring services available: Paper Review, Live Chat, and Tutor E-mail. Click on the Writing Center & Library tab in the left-navigation menu, in your online course, to learn more about these tutoring options and how to get help with your writing.Late Policy: Written assignments (essays, journals, presentations) are due on the specified days in the course. Written assignments will be subject to a late penalty of up to 10% per day up to three days late. If written assignments are submitted after 72 hours past the due date, instructors can give a penalty up to and including a grade of zero for the assignment.Carefully review the Grading Rubric for the criteria that will be used to evaluate your assignment.

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