#### Description of this paper

##### Instructions For this project, you will write a...

**Description**

Solution

**Question**

Instructions For this project, you will write a paper that involves designing, conducting, and analyzing results from your own experiment to test the sensory discrimination of one of your friends. Choose a friend who claims to be able to tell the difference between two very similar objects. You are free to choose the two objects, however here are some ideas to get you thinking along the right lines: Coke vs. Pepsi, Regular vs. Decaf coffee, Sweet 'n' Low vs. Equal sweetener, butter vs. margarine, or Ghiradelli chocolate vs. Hershey?s chocolate. Which you choose depends on whoever your ?expert? testing subject is. You will need to find an expert on your own, and will need to supply your own materials. The cost of your experiment will obviously depend primarily on the objects to be tested; testing to see if the subject can discern between bottled water and tap water will only cost a couple dollars, testing to see if the subject can discern between different brands of caviar will get pricey fast! Your paper should consist of a single document in Microsoft Word format. After you have completed your paper, you must submit it to Turnitin.com. Login and password details for Turnitin.com can be found in the classroom. 1. First, you should brainstorm to find a friend who is either a self-proclaimed expert or has some food/beverage related idiosyncracy(1). 2. Determine a protocol for administering the test a) What should be done about random variations in the items to be tested? For example, how do you prevent temperature change in the product, or to make sure each cup of coffee is equally sweet or has the same amount of cream? Before conducting your experiment, carefully lay out the procedure for administering the test, such as how the coffee will be made, how the wine will be decanted, and so forth. This is related to the important issue of ensuring that each trial is independent (i.e. the previous trials aren?t tainting your taster?s sense of taste). If you have ever been to a wine tasting, you?ll notice that you can tell the difference between the first few sips of wine, but once you get to the 11th and 12th glass, it?s all sort of a blur (and not due to inebriation!). Carefully consider how you will attempt to overcome this problem. b) How many trials should be used in the test (for this, see Levine Chapter 7 and 8.4, or read up on the Fisher exact test)? Should they be paired or independent(2)? In what order should the items be presented? Should the experiment be run in one sitting or spaced out over a number of days? Done properly, the experiment should be designed such that if the expert has no expert skills, the result will be wholly governed by chance. The number and ordering of the trials should allow an expert to prove his or her abilities while simultaneously preventing a fraud from succeeding. You will want to keep the binomial distribution in mind when making these decisions. c) What conclusion could be drawn from a perfect score or from a test with one or more errors? For the design you are considering, list all possible results of the experiment. For each possible result, decide in advance what conclusion you will make if it occurs. In determining this mapping of outcomes to conclusions, consider the probability that someone with no powers of discrimination could wind up with each outcome. You may want to make adjustments in your design to increase the sensitivity of your experiment. For example, if someone can?t distinguish decaf coffee from regular, then just by guessing, he/she should still be right half of the time and there will be a small chance, which you should calculate, of being right 100% of the time. On the other hand, if the taster possesses some, but not perfect, skill in differentiation, he or she will make some mistakes. 3. Write out an instruction sheet for your experimental process. Conduct a ?dress rehearsal? on somebody other than your subject to work out kinks in the process. After the practice run, determine whether or not you want to make changes in your instruction sheet to address any problems that arose. This practice run is an extremely important step; many people make big mistakes in their first attempt and historically, students who have taken this step seriously have scored much more highly on this project than those who do not. 4. You should now be ready to run your experiment. Record your results CAREFULLY, and note any unusual occurrences in the experimental process. It may be a good idea to keep track of the order in which the samples are served to your subject. 5. Numerically, summarize the results and analyze the data. Do they support or contradict the claim that the subject possesses no sensory discrimination? Use your list of all possible events and subsequent actions to come to a conclusion. Discuss the reasons behind the decision that you have made. For ideas on how to analyze the data, see Levine Ch. 9 or use the Fisher exact test. 6. What changes would you make to your experimental process if you had the opportunity to do it again? Why didn't you pick these issues up when you did your practice run? You are to work individually on this assignment. You can find definitions of academic dishonesty and plagiarism at http://www.umuc.edu/policy/academic/aa15025.shtml, along with the procedures I will follow should I suspect any transgressions of such nature. Suggested Report Format with Headings Purpose of the study The purpose of the study formally explains why the study was important to conduct and write the null and alternative hypotheses of the study (see Levine Ch. 9.1 and read the lecture material in the classroom from session 8). Method The Method section explains how the study was conducted to collect data. The section should include the following: 1. Participants of the study. Who are they? Where did you get the participants for the study? Which sampling design was used to select the participants? 2. Experimental design. Which experimental/sampling design was used in the study? 3. Data Collection. Explain the method used to collect data. 4. Data Analysis. For hypothesis testing, explain how you plan to calculate the data. 5. Step-by-step procedure. Explain the explicit steps from beginning to end for conducting the study. If another researcher wants to replicate the study, the directions must contain precise information for conducting the study. Data Analysis Show the results of your data analysis, including tables and charts as necessary. You should also discuss, in plain English, the results of the data calculation, both in terms of magnitude and significance. Discussion Discuss what you learned from the data collected. Did the results support or not support the null hypothesis? Appendix Place the charts, tables, and other relevant documents in an appendix at the end of your paper. Your paper should contain between 5 and 7 pages of text, plus any additional charts/tables/graphs found in the appendix. (1) While something simple like butter vs. margarine or bottled water vs. tap water is a reasonable topic, students who have been more creative in their subject selection have found this paper to be rather enjoyable. Some examples of creative subjects: Testing to see is one call tell the difference between freshly grated parmesan cheese and the Kraft brand parmesan cheese (in the green tube) One individual's wife maintained that the white candies from a box of Good 'N' Plenty candy did not taste as good as the pink candies. The test was to see if his wife could tell the difference. One individual had a friend who ran a wine tasting social group. She tested whether or not her friend could discern between red and white wine by bouquet alone. Note that this does not say that one of the more "creative" ideas will necessarily make for a better experiment, paper, or grade. You are more likely, however, to enjoy the process of conducting the experiment and analyzing the data should you put serious thought into your test subject. (2) Paired vs. independent?In the context of a Coke vs. Pepsi expert, for example, in a paired test, for each trial you present one of each type at the same time and tell your subject to identify which one is Coke and which is Pepsi. If you were doing independent trials, in each trial they?d get exactly one cup, filled with either Coke or Pepsi, and be asked to identify which it is.,attaching chapter 9,any feed back,Natalia, 1) cannot open the 2 files with extension spv 2) the word document is not using the specified research as it has to be sensory analysis of wine tasting with one subject I have only today to use this as a sample, can you please re send with file extensions of word/excel and with the above specifications- I had uploaded my attachments with the outlines, etc with the question.,Also, if you could use chapter 9 as the basis. I had uploaded it earlier as well. if the document can be in word and excel that would be good. I do have data analysis and PHstat for excel available. If you need anything else please let me know. I am attaching,natalia, My problem as stated in the question is on conducting an experiment for sensory discrimination using null hypothesis test. The attached document and excel file has lot more attributes and does not have yes or no answer. Is it possible to work on the outline I had submitted. I have to submit it soon- can you get to it soon as I next hr or so I will start writing from scratch. I am attaching my draft paper so far. The one you send does not address the problem. I have to use null hypothesis such as My husband can detect the difference between expensive red wine and cheap red wine and use one of the test methods such as p-value test, Ztest in the experiment. Regards, Sunita,Resubmitting the requirement for paper again. 1) it has to be a sensory test such as to differentiate between two similar products 2) I am attaching my draft paper ----For this project, you will write a paper that involves designing, conducting, and analyzing results from your own experiment to test the sensory discrimination of one of your friends. Choose a friend who claims to be able to tell the difference between two very similar objects. You are free to choose the two objects, however here are some ideas to get you thinking along the right lines: Coke vs. Pepsi, Regular vs. Decaf coffee, Sweet 'n' Low vs. Equal sweetener, butter vs. margarine, or Ghiradelli chocolate vs. Hershey?s chocolate. Which you choose depends on whoever your ?expert? testing subject is. You will need to find an expert on your own, and will need to supply your own materials. The cost of your experiment will obviously depend primarily on the objects to be tested; testing to see if the subject can discern between bottled water and tap water will only cost a couple dollars, testing to see if the subject can discern between different brands of caviar will get pricey fast! Your paper should consist of a single document in Microsoft Word format. After you have completed your paper, you must submit it to Turnitin.com. Login and password details for Turnitin.com can be found in the classroom. 1. First, you should brainstorm to find a friend who is either a self-proclaimed expert or has some food/beverage related idiosyncracy(1). 2. Determine a protocol for administering the test a) What should be done about random variations in the items to be tested? For example, how do you prevent temperature change in the product, or to make sure each cup of coffee is equally sweet or has the same amount of cream? Before conducting your experiment, carefully lay out the procedure for administering the test, such as how the coffee will be made, how the wine will be decanted, and so forth. This is related to the important issue of ensuring that each trial is independent (i.e. the previous trials aren?t tainting your taster?s sense of taste). If you have ever been to a wine tasting, you?ll notice that you can tell the difference between the first few sips of wine, but once you get to the 11th and 12th glass, it?s all sort of a blur (and not due to inebriation!). Carefully consider how you will attempt to overcome this problem. b) How many trials should be used in the test (for this, see Levine Chapter 7 and 8.4, or read up on the Fisher exact test)? Should they be paired or independent(2)? In what order should the items be presented? Should the experiment be run in one sitting or spaced out over a number of days? Done properly, the experiment should be designed such that if the expert has no expert skills, the result will be wholly governed by chance. The number and ordering of the trials should allow an expert to prove his or her abilities while simultaneously preventing a fraud from succeeding. You will want to keep the binomial distribution in mind when making these decisions. c) What conclusion could be drawn from a perfect score or from a test with one or more errors? For the design you are considering, list all possible results of the experiment. For each possible result, decide in advance what conclusion you will make if it occurs. In determining this mapping of outcomes to conclusions, consider the probability that someone with no powers of discrimination could wind up with each outcome. You may want to make adjustments in your design to increase the sensitivity of your experiment. For example, if someone can?t distinguish decaf coffee from regular, then just by guessing, he/she should still be right half of the time and there will be a small chance, which you should calculate, of being right 100% of the time. On the other hand, if the taster possesses some, but not perfect, skill in differentiation, he or she will make some mistakes. 3. Write out an instruction sheet for your experimental process. Conduct a ?dress rehearsal? on somebody other than your subject to work out kinks in the process. After the practice run, determine whether or not you want to make changes in your instruction sheet to address any problems that arose. This practice run is an extremely important step; many people make big mistakes in their first attempt and historically, students who have taken this step seriously have scored much more highly on this project than those who do not. 4. You should now be ready to run your experiment. Record your results CAREFULLY, and note any unusual occurrences in the experimental process. It may be a good idea to keep track of the order in which the samples are served to your subject. 5. Numerically, summarize the results and analyze the data. Do they support or contradict the claim that the subject possesses no sensory discrimination? Use your list of all possible events and subsequent actions to come to a conclusion. Discuss the reasons behind the decision that you have made. For ideas on how to analyze the data, see Levine Ch. 9 or use the Fisher exact test. 6. What changes would you make to your experimental process if you had the opportunity to do it again? Why didn't you pick these issues up when you did your practice run? You are to work individually on this assignment. You can find definitions of academic dishonesty and plagiarism at http://www.umuc.edu/policy/academic/aa15025.shtml, along with the procedures I will follow should I suspect any transgressions of such nature. Suggested Report Format with Headings Purpose of the study The purpose of the study formally explains why the study was important to conduct and write the null and alternative hypotheses of the study (see Levine Ch. 9.1 and read the lecture material in the classroom from session 8). Method The Method section explains how the study was conducted to collect data. The section should include the following: 1. Participants of the study. Who are they? Where did you get the participants for the study? Which sampling design was used to select the participants? 2. Experimental design. Which experimental/sampling design was used in the study? 3. Data Collection. Explain the method used to collect data. 4. Data Analysis. For hypothesis testing, explain how you plan to calculate the data. 5. Step-by-step procedure. Explain the explicit steps from beginning to end for conducting the study. If another researcher wants to replicate the study, the directions must contain precise information for conducting the study. Data Analysis Show the results of your data analysis, including tables and charts as necessary. You should also discuss, in plain English, the results of the data calculation, both in terms of magnitude and significance. Discussion Discuss what you learned from the data collected. Did the results support or not support the null hypothesis? Appendix Place the charts, tables, and other relevant documents in an appendix at the end of your paper. Your paper should contain between 5 and 7 pages of text, plus any additional charts/tables/graphs found in the appendix. (1) While something simple like butter vs. margarine or bottled water vs. tap water is a reasonable topic, students who have been more creative in their subject selection have found this paper to be rather enjoyable. Some examples of creative subjects: Testing to see is one call tell the difference between freshly grated parmesan cheese and the Kraft brand parmesan cheese (in the green tube) One individual's wife maintained that the white candies from a box of Good 'N' Plenty candy did not taste as good as the pink candies. The test was to see if his wife could tell the difference. One individual had a friend who ran a wine tasting social group. She tested whether or not her friend could discern between red and white wine by bouquet alone. Note that this does not say that one of the more "creative" ideas will necessarily make for a better experiment, paper, or grade. You are more likely, however, to enjoy the process of conducting the experiment and analyzing the data should you put serious thought into your test subject. (2) Paired vs. independent?In the context of a Coke vs. Pepsi expert, for example, in a paired test, for each trial you present one of each type at the same time and tell your subject to identify which one is Coke and which is Pepsi. If you were doing independent trials, in each trial they?d get exactly one cup, filled with either Coke or Pepsi, and be asked to identify which it is.,cut and paste of paper- if you did not get the attachment: --- Introduction Sensory discrimination tests are used in sensory analysis to determine if there is a perceptible difference between two or more similar products (Lawless, 2010, PP. 80). Sensory research is important to understand attributes of a product important to consumers in its acceptance, point out the shortcomings of a product, or warrant further research. Hypothesis testing involves using an inferential procedure to examine credibility of a hypothesis about a population based on the probability of the sample data ((Levine et al., 2011, PP. 298). The sampling distribution tells us the degree of variability to expect with regard to some statistic. This allows us to see if our sample statistics varies a lot from the random error that we can expect from sampling from a population with a particular value. There are two type of hypothesis in statistics: null hypothesis which is the one you are attempting to reject or refute. Null indicates ?nothing happened?, in that our data are from assumed distribution. Null does not indicate a zero effect hypothesis and the symbols used for Null Hypothesis is Ho (Levine et al., 2011, PP. 299). The alternative hypothesis is that data does not come from assumed distribution and its symbol is H1. The null and alternative hypothesis deal with theories about parameter of interest, which is the parameter you are trying to make conclusion about. Null hypothesis testing (NHST) is used to get rid of errors beforehand. The null hypothesis (H0) is the statement that is assumed to be true unless sufficient evidence is gathered to reject the hypothesis. NHST is a hypothesis about a population parameter. The purpose of the study is to test the viability of a null hypothesis in the light of experiment data. Depending on the data, the null hypothesis will or will not be rejected. Null hypothesis is often a reverse of what the experimenter believes In this study we want to know if people can discriminate between expensive red wine and cheap red wine. For this I conducted an experiment on my husband who is a wine connoisseur. For purposes of the test, the null hypothesis, a representation of what I have tentatively assumed about the value of the parameter is that I believe my husband Vic knows the difference between the expensive red wines and cheap red wines due the difference in the attributes such taste, smoothness, and richness. Ho=1 Vic can find detectable difference between expensive & cheap red wines H1 ? 1 Vic cannot find detectable difference between expensive & cheap red wines. Methodology Make a claim, sample the population and find the sample mean. If the sample mean is close to population mean the null hypothesis is not rejected. If the sample mean is far from the populations mean the null hypothesis is rejected. We can use several statistical methods to analyze the data such as Z test hypothesis (population standard deviation is known), t test (where population standard deviation ? (?) is not known). ?P-value approach to testing is the probability of obtaining a test statistic equal to or more extreme than sample? The p-value is also called observed level of significance (Levine et al., 2011, PP. 305). It is the smallest value of Subject & Product Subject: My husband Products: 2 Red wines- 2 Buck Chuck (HGV-KJ) Kendall Jackson (2008) (BJV-2BC) Sample Size: 15 (one of each kind of wine) over period of 15 days Test method: p test Set up Procedure Sensory tests have to be conducted under controlled conditions in order to reduce bias on how the subject views the product. The sensory room has to be free from all distractions such as sound odor, so that it does not influence the subject?s view of the product. The test was conducted using standardized protocols: 1. Experiment was explained to Vic with clear instructions on the objective 2. Established that the test would be conducted over 15 days precisely at 6:30 Pm before dinner time 3. Established that ? cup of wine would be poured in each glass 4. The wine bottle will be opened 30 minutes prior to tasting 5. Sip of water was given at room temperature Material Used: ? 15 similar wine glasses ? Water at room temperature ? Data sheet for recording observations ? 15 water glasses Instruction Sheet Sensory Test of wines Please take a sip of water before tasting each wine. Place an X under the Wine glass which tastes better Left ___________________ Right____________________________ Significance Level Significance level is the value that ?represents the boundary between results that are statistically significant and results that are not statistically significant? (Larose, 2009. 469). By setting a benchmark we establish criteria known as level of significance or alpha level. The most commonly used alpha levels are .05 (5%) and .01 (1%). These levels of significance correspond with specific z scores, but depend on if hypothesis is directional or non-directional. Non directional hypotheses--? 2-tailed test ? 0.05 level -------> Z critical = +/- 1.96 ? 0.01 level -----> Z critical = +/- 2.58 Directional hypotheses--? 1-tailed test ? 0.05 level -------> Z critical = +/- 1.65 ? 0.01 level -----> Z critical = +/- 2.33 For purposes of this experiment a significance level of .05 will be chosen, which leaves a 5% chance of the null hypothesis being true, or a type 1 error. In this setting, a type 1 error corresponds to Vic finding any difference between 2 buck chuck and Kendall Jackson. Parameter The test will have a preference. The preference will be recorded as probability of my husband knowing the difference between expensive red wines and cheap red wines. This is P(KJ). If the null hypotheses was true then P(KJ) = P(null) = 0.5. If the alternate hypotheses is true then P(KJ) > P(null) = 0.5 Evaluate Data KJ 2BC 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 1 0 1 0=unable to identify the expensive red wines 1 = able to identify the red wines Sample size= N=15 Total Population = 30 No Of times Vic Identified each wine (X1) Sample proportion Kendall Jackson (KJ) 5 P1= X1/NI=5/15=.3333 2 Buck Chuck 10 P1= X1/N1=10/15 = .6667 P1= proportion of the number of times Vic is able to identify the taste of Kendall Jackson P2= proportion of the number of times Vic is able to identify the taste of 2 Buck Chuck The hypothesis to be tested are: H0: P1= P2=.05 Sample size= 15 Sample proportion of KJ = P1=X1/N1 = 5/15 = .3333 Sample proportion of 2BC= P2 = X2/N2=10/15 = .6667 Calculate sample size determination for the MEAN using PSTAT: Data Population Standard Deviation 0.48 Sampling Error 0.05 Confidence Level 95% Intemediate Calculations Z Value -1.9600 Calculated Sample Size 354.0288 Result Sample Size Needed 355 Sample size determination for the proportion Confidence Interval for the mean using PHSTAT: Data Sample Standard Deviation 0.487950036 Sample Mean 0.666666667 Sample Size 15 Confidence Level 95% Intermediate Calculations Standard Error of the Mean 0.125988158 Degrees of Freedom 14 t Value 2.1448 Interval Half Width 0.2702 Confidence Interval Interval Lower Limit 0.40 Interval Upper Limit 0.94 Pooled estimate of the common value of P P= 5/15 +10/15 = .05 Performed the t test for the hypothesis of the mean: t Test for Hypothesis of the Mean Data Null Hypothesis ?= 0 Level of Significance 0.05 Sample Size 15 Sample Mean 0.666666667 Sample Standard Deviation 0.487950036 Intermediate Calculations Standard Error of the Mean 0.1260 Degrees of Freedom 14 t Test Statistic 5.2915 Two-Tail Test Lower Critical Value -2.1448 Upper Critical Value 2.1448 p-Value 0.0001 Reject the null hypothesis t Test for Hypothesis of the Mean when =1 Data Null Hypothesis ?= 1 Level of Significance 0.05 Sample Size 15 Sample Mean 0.666666667 Sample Standard Deviation 0.487950036 Intermediate Calculations Standard Error of the Mean 0.1260 Degrees of Freedom 14 t Test Statistic -2.6458 Two-Tail Test Lower Critical Value -2.1448 Upper Critical Value 2.1448 p-Value 0.0192 ANOVA: Levene Test Calculations c 2 SUMMARY n 30 Groups Count Sum Average Variance KJ 15 5 0.333333333 0.2381 2BC 15 5 0.333333333 0.2381 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 0.0000 1 0.0000 0.0000 1.0000 4.1960 Within Groups 6.6667 28 0.2381 Total 6.6667 29 Level of significance 0.05 The test statistics is calculated as : Z=(.03333 - .06667) / .182574186 = 1.8.8257 The P value is P(Z>-1.8257) ? 0.066 Step5 draw conclusions Two types of errors can occur in hypothesis testing-Type I error is committed when we reject the null hypothesis when it is true. Type II error is committed when we the null hypothesis when it is true. Since p- value is large, the test fail to reject H0 (at a = 0.05 level of significance) The sample data does not provide conclusive evidence that Vic is able to differentiate between the taste of Kendall Jackson and 2 Buck Chuck. Null Hypothesis significant testing (NHST) has been criticized heavily on the basis that to draw inference from the data, NHST must be complemented with additional methods of analysis such as use of confidence interval, degree of association of independent and dependent variables. These methods should be complements of NHST, rather than substitutes, as they do not test the strength of evidence against null Hypothesis (Lawless, 2010, PP. 79-82). A statistical hypothesis testing is a method of making decisions using experimental data. In statistics this result is called statistically significant if it is unlikely to have occurred by chance. The phrase "test of significance" was coined by Ronald Fisher: "Critical tests of this kind may be called tests of significance, and when such tests are available we may discover whether a second sample is or is not significantly different from the first." If the data do not contradict the null hypothesis, then no conclusion is made. In this case, the null hypothesis could be true or false; the data gives insufficient evidence to make any conclusion as in the experiment conducted for the wine tasting. Level of significance reflects the maximum probability of committing an error, before samples are taken researcher specifics the maximum probability of committing an error called level of significance. References: how to use fisher exact test in sensory discrimination Bi, J. (2006). Sensory Discrimination Tests and Measurements|Statistical Principles, Pro- cedures and Tables. Blackwell Publishing. ENNIS, J. M., & JESIONKA, V. (2011). THE POWER OF SENSORY DISCRIMINATION METHODS REVISITED. Journal Of Sensory Studies, 26(5), 371-382. doi:10.1111/j.1745-459X.2011.00353.x Gross, J. (1995). Testing data for consistency with revealed preference. Review Of Economics & Statistics, 77(4), 701. Fisher, R. A. (1922). "On the interpretation of ?2 from contingency tables, and the calculation of P". Journal of the Royal Statistical Society 85 (1): 87?94. doi:10.2307/2340521. JSTOR 2340521. Lawless, H.T. and Glatter,S. 1990. Consistency of multidimensional scaling models dervived from odor sorting. Journal of Sensory studies, 5,217-230. Jeffrey A Gliner, Jerry J Vaske, George A Morgan (2001) Human Dimensions of Wildlife 6 (4) p. 291-301 Meilgaard, M, Civille, GV, Carr, BT. 1999. Sensory Evaluation Techniques. 3rd ed. Boca Raton: CRC Press LLC.,need help with putting the outline together based on requirement using P value test and graphs for sensory discrimination. call me at 561-213-7864 if you need further clarifications,please let me know by 7 Am as I have worked most of it out myself- would still prefer a professional looking version if you can get it to me by 7 AM EST tomorrow it will be great. I think we need to use the T value Two tailed test If I state my hypothesis as Ho=.60- Vic can detect the difference 60% of the time H1 ? .60 Vic cannot find detectable difference 60% of the time and If tSTAT is within the critical T values then do not reject H0, else reject Ho using phstate the answer is: data KJ 1 0 1 1 1 0 1 0 0 1 1 1 1 1 1 Answer: t Test for Hypothesis of the Mean Data Null Hypothesis m= 0.6 Level of Significance 0.05 Sample Size 15 Sample Mean 0.7333 Sample Standard Deviation 0.457738 Intermediate Calculations Standard Error of the Mean 0.1182 Degrees of Freedom 14 t Test Statistic 1.1279 Two-Tail Test Lower Critical Value -2.1448 Upper Critical Value 2.1448 p-Value 0.2783 Do not reject the null hypothesis,let me know if the answer is available as I have to submit by 12 noon EST,all I can see is the z test- which is fine but you did not re-write word document- the attached word document is the cut and paste of my postings. are you going to reword? I cannot use this,I have an extension till 5 PM EST. Can you please look over the attached document. I would 1) refine the paper with additional graphs, corrections 2) suggest ways to make it more precise 3) references for APA style 4) ensure it follows guide lines posted earlier,are you still working at it?,Sorry, cannot use it as the deadline was past due

Paper#9929 | Written in 18-Jul-2015

Price :*$25*