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Quirk, S. Excel for Statistics. Quirk, J. Springer International Publishing. Additional Statistics books by Dr. Tom Quirk that have been published by Springer T. Thomas J Quirk. Walmart Tell us if something is incorrect. Only 5 left! Add to Cart. Free delivery. Arrives by Friday, Oct Pickup not available.
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If you want to learn more about this idea, you can consult a good statistics book e. For example: 1. For example, if you have 14 people in your research study, the value of t is 2. If you have 26 people in your research study, the value of t is 2. If you have more than 40 people in your research study, the value of t is always 1. You will recall from Chap. You will also recall from Chap. General Motors claimed that its Chevy Impala Anonymous achieved 28 miles per gallon mpg on the highway.
A billboard in St. Suppose that you work for Ford Motor Co. Your research study produces the results given in Fig. Center these numbers in Column A. Then, widen columns A and B by making both of them twice as wide as the original width of column A. Then, widen column C so that it is three times as wide as the original width of column A so that your table looks more professional.
Mean value upper limit Conclusion: Now, align the labels underneath the picture of the confidence interval so that they look like Fig. Note that this TINV formula uses 24 since 24 is one less than the sample size of 25 i. Note that D10 is the mean, while D16 is the standard error of the mean.
The above formula gives the lower limit of the confidence interval, Now, use number format two decimal places in your Excel spreadsheet for the mean, standard deviation, standard error of the mean, and for both the lower limit and the upper limit of your confidence interval. If you printed this spreadsheet now, the lower limit of the confidence interval Do that now, and notice that the dotted line to the right of Your research study accepted the claim that the Chevy Impala did get 28 mpg.
The average miles per gallon in your study was We can test these guesses using statistical formulas to see if our predictions come true in the real world. So, in order to perform these statistical tests, we must first state our hypotheses so that we can test our results against our hypotheses to see if our hypotheses match reality. So, how do we generate hypotheses in business?
For example, if we are interested in studying 18—24 year-olds in St. Louis as our target market, and we select a sample of people in this age group in St. Louis, depending on how we select our sample, we are hoping that our results of this study are useful in generalizing our findings to all 18—24 year-olds in St. Louis, and not just to the particular people in our sample.
The entire group of 18—24 year-olds in St. Louis would be the population that we are interested in studying, while the particular group of people in our study is called the sample from this population. In testing our hypotheses, we are trying to decide which one of two competing hypotheses about the population mean we should accept given our data set. Statistics textbooks typically refer to the null hypothesis with the notation: H0. The research hypothesis is typically referred to with the notation: H1, and it is sometimes called the alternative hypothesis.
The null hypothesis is what we accept as true unless we have compelling evidence that it is not true. The research hypothesis is what we accept as true whenever we reject the null hypothesis as true. This is similar to our legal system in America where we assume that a supposed criminal is innocent until he or she is proven guilty in the eyes of a jury. Our null hypothesis is that this defendant is innocent, while the research hypothesis is that he or she is guilty. Since both the null hypothesis and the research hypothesis cannot both be true, the task of hypothesis testing using statistical formulas is to decide which one you will accept as true, and which one you will reject as true.
These rating scales are typically 5-point, 7-point, or point scales, although other scale values are often used as well. Objective: To decide on the null hypothesis and the research hypothesis whenever rating scales are used. In the above example, since 4 is the number in the middle of the scale i. The job of the business researcher, then, is to decide which of these two hypotheses, the null hypothesis or the research hypothesis, he or she will accept as true given the data set in the research study.
In the spaces in Fig. Here are the answers to these three questions: 1. The null hypothesis is 3, and the research hypothesis is not equal to 3 on this 5-point scale i. The null hypothesis is 4, and the research hypothesis is not equal to 4 on this 7-point scale i.
The null hypothesis is 5. Find the standard error of the mean s. In practice, this is more difficult than it sounds because you are trying to summarize the result of your statistical test in simple English that is both concise and accurate so that someone who has never had a statistics course such as your boss, perhaps can understand the conclusion of your test. This is a difficult task, and we will give you lots of practice doing this last and most important step throughout this book.
Rule 3: Write the conclusion in plain English so that the reader can understand it even if that reader has never taken a statistics course. Objective: To state the result when you accept H0 3. This is a basic rule we are using in this chapter for every problem.
The process of writing the conclusion when you accept H0 is relatively straightforward since you put into words what you said when you wrote the null hypothesis. Note that this conclusion says that the mpg was less than 34 mpg because the sample mean was only 31 mpg. Case 2: Suppose that you have been hired as a consultant by the St. Louis last month.
You have decided to practice your data analysis skills on Question 7 given in Fig. Suppose that your analysis produced the following confidence interval for this item on the survey. Value Result: Since the reference value is outside the confidence interval, we reject the null hypothesis and accept the research hypothesis.
Case 3: Suppose that Marriott Hotel at the St. Value 5. Louis Airport Marriott Hotel last week rated their check-in speed in a survey as significantly positive. The three practice problems at the end of this chapter will give you additional practice in stating the conclusion of your result, and this book will include many more examples that will help you to write a clear and accurate conclusion to your research findings. We are consistent in the use of these words so that you can understand the concept underlying hypothesis testing. However, there are many other ways to summarize the result of a hypothesis test, and all of them are correct theoretically, even though the terminology differs.
If you are taking a course with a professor who wants you to summarize the results of a statistical test of hypotheses in language, which is different from the language we are using in this book, do not panic!
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If you understand the concept of hypothesis testing as described in this book, you can then translate your understanding to use the terms that your professor wants you to use to reach the same conclusion to the hypothesis test. Statisticians and professors of business statistics all have their own language that they like to use to summarize the results of a hypothesis test. There is no one set of words that these statisticians and professors will ever agree on, and so we have chosen the one that we believe to be easier to understand in terms of the concept of hypothesis testing.
The null hypothesis is rejected. Suppose that you have been asked by the manager of the St. Louis Post-Dispatch to analyze the data from a recent survey of past subscribers who have canceled their newspaper subscription in the past 3 months. A random sample of this group was called by phone and asked a series of questions about the newspaper. The hypothetical data for survey question 4 appear in Fig.
Is this a reasonable price to charge based on the results of this survey question? Label your answers. Use currency format two decimal places for the mean, standard deviation, and standard error of the mean. Use currency format two decimal places. You want to test out your Excel skills on a small sample of managers with one item from the survey. You select a random sample of managers and the hypothetical data from Item 24 are given in Fig. Label your answers, and use two decimal places for the mean, standard deviation, and standard error of the mean b Enter the null hypothesis and the research hypothesis for this item on your spreadsheet.
Label your answers on your spreadsheet. Use two decimal places for the lower limit and the upper limit of the confidence interval. Suppose that you have been asked to conduct three focus groups in different cities with adult women ages 25—44 to determine how much they liked a new design of a blouse that was created by a well-known designer. You conduct a 1-hour focus group discussion with three groups of adult women in this age range, and the last question on the survey at the end of the discussion period produced the hypothetical results given in Fig.
Label your answers, and use two decimal places and currency format for the mean, standard deviation, and standard error of the mean b Enter the null hypothesis and the research hypothesis for this item onto your spreadsheet. Use two References d e f g h 65 decimal places in currency format for the lower limit and the upper limit of the confidence interval.
Enter the result of the test on your spreadsheet. Enter the conclusion of the test in plain English on your spreadsheet. Print your final spreadsheet so that it fits onto one page if you need help remembering how to do this, see the objectives at the end of Chap. Draw a picture of the confidence interval, including the reference value, onto your spreadsheet. Save the final spreadsheet as: blouse9 References Anonymous. Automotive News. Detroit: Dec. Black, K. Business Statistics: for Contemporary Decision Making 6th ed.
Keller, G. Statistics for Management and Economics 8th ed. Levine, D. Statistics for Managers using Microsoft Excel 6th ed. McDaniel, C. Marketing Research 8th ed. Salkind, N. Weiers, R. Zikmund, W.
Excel 2010 for business statistics a guide to solving practical business problems
Exploring Marketing Research 10th ed. Chapter 4 One-Group t-Test for the Mean In this chapter, you will learn how to use one of the most popular and most helpful statistical tests in business research: the one-group t-test for the mean.
The standard error of the mean equals the standard deviation divided by the square root of n the sample size. There are seven steps in this process: T. For example, the absolute value of 2. And the absolute value of minus 2. This becomes important when you are using the t-table in Appendix E of this book. We will discuss this table later when we get to Step 5 of the one-group t-test where we explain how to find the critical value of t using Appendix E.
To use this formula, you need to follow these steps: 1. Then take your answer from the above step, and divide your answer by the standard error of the mean for your research study you will remember that you learned how to find the standard error of the mean in Chap. The number you get after you complete the above step is the value for t that results when you use the formula stated above. For example, if you have 27 people in your research study, the critical value of t is 2.
If you have 38 people in your research study, the critical value of t is 2. If you have more than 40 people in your research study, the critical value of t is always 1. Thus, values of t that are to the right of this zero point are positive values that use a plus sign before them, and values of t that are to the left of this zero point are negative values that use a minus sign before them.
Thus, some values of t are positive, and some are negative. However, every statistics book that includes a t-table only reprints the positive side of the t-curves because the negative side is the mirror image of the positive side; this means that the negative side contains the exact same numbers as the positive side, but the negative numbers all have a minus sign in front of them. Therefore, to use the t-table in Appendix E, you need to take the absolute value of the t-value you found when you use the t-test formula since the t-table in Appendix E only has the values of t that are the positive values for t.
Therefore, the value for t in the t-table in Appendix E 4. Since the absolute value of t that you found in the t-test formula is greater than the critical value of t in Appendix E, you reject the null hypothesis, and accept the research hypothesis. In practice, this is more difficult than it sounds because you are trying to summarize the result of your statistical test in simple English that is both concise and accurate so that someone who has never had a statistics course such as your boss, perhaps can understand the result of your test. If you have read this far, you are ready to sit down at your computer and perform the one-group t-test using Excel on some hypothetical data from the Guest Satisfaction Survey used by Marriott Hotels.
Louis to analyze the data from a Guest Satisfaction survey that they give to all customers to determine the degree of satisfaction of these customers for various activities of the hotel. Important note: You would need to use this test for each of the survey items separately. Suppose that the hypothetical data for Item 7 from last week at the St. Louis Marriott Hotel were based on a sample size of guests who had a mean score on this item of 6. Objective: To analyze the data for each question separately using the onegroup t-test for each survey item.
Now, use two decimal places for both the s. Now, write the following sentence in D36—D39 to summarize the result of the t-test: D Since the absolute value of t of 4. Enter the null hypothesis and the research hypothesis by hand on your spreadsheet Fig.
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Louis Marriott Hotel Guests rated the Front Desk Clerks as friendly last week, and this result was probably not obtained by chance. Is this a correct statement? Both of these tests produce the same result and the same conclusion from the data set! Both of these tests are explained in this book because some managers prefer the confidence interval about the mean test, others prefer the one-group t-test, and still others prefer to use both tests on the same data to make their results and conclusions clearer to the reader of their research reports.
Since we do not know which of these tests your manager prefers, we have explained both of them so that you are competent in the use of both tests in the analysis of statistical data. Suppose that you have selected a random sample of rating forms submitted by new car purchasers either online or through the mail for the St. Louis Subaru dealer in the past week and that you have prepared the hypothetical table in Fig. Use number format 2 decimal places for the mean, standard deviation, and standard error of the mean.
Suppose that you work in the Human Resources department of your company and that top management has asked your department to conduct a Morale Survey of managers to determine their attitude toward working in this company. To check your Excel skills, you have drawn a random sample of the results of the survey from the managers on one question, and the data from Item 35 appear in Fig.
Suppose that you have been hired as a marketing consultant by the Missouri Botanical Garden and have been asked to redesign the Comment Card survey that they have been asking visitors to The Garden to fill out after their visit. The hypothetical results of a recent week for Question 10 of your revised survey appear in Fig. Foster, D. Basic Business Statistics: A Casebook. We will now change gears and deal with the situation in which you are measuring two groups of people instead of only one group of people.
Whenever you have two completely different groups of people i. The assumptions underlying the two-group t-test are the following Zikmund and Babin : 1 both groups are sampled from a normal population, and 2 the variances of the two populations are approximately equal. Note that the standard deviation is merely the square root of the variance. This book only deals with two groups that are independent of one another so that no person is in both groups of data. When you are testing for the difference between the means for two groups, it is important to remember that there are two different formulas that you need to use depending on the sample sizes of the two groups: 1.
Use Formula 1 in this chapter when both of the groups have more than 30 people in them 2. Use Formula 2 in this chapter when either one group, or both groups, have sample sizes less than 30 people in them. We will illustrate both of these situations in this chapter. But, first, we need to understand the steps involved in hypothesis-testing when two groups of people are involved before we dive into the formulas for this test.
If you define which group is Group 1 and which group is Group 2, you can use these subscripts in your computations without having to write out the names of the groups. If you call the Coke group, Group 1, and the Pepsi group, Group 2, this makes it much easier to refer to the groups because it saves you writing time.
As a second example, you could be comparing the test market results for Kansas City versus Indianapolis, but if you had to write out the names of those cities whenever you wanted to refer to them, it would take you more time than it would if, instead, you named one city, Group 1, and the other city, Group 2. Note, also, that it is completely arbitrary which group you call Group 1, and which Group you call Group 2. You will achieve the same result and the same conclusion from the formulas however you decide to define these two groups. After the research study was completed, suppose that the Coke group had 52 boys in it, their mean taste rating was 55 with a standard deviation of 7, while the Pepsi group had 57 boys in it and their average taste rating was 64 with a standard deviation of The formulas for analyzing these data to determine if there was a significant different in the taste rating for teenage boys for these two brands require you to use six numbers correctly in the formulas: the sample size, the mean, and the standard deviation of each of the two groups.
All six of these numbers must be used correctly in the formulas if you are to analyze the data correctly. If you create a table to summarize these data, a good example of the table, using both Step 1 and Step 2, would be the data presented in Fig. Note that you could just as easily call Group 1 the Pepsi group and Group 2 the Coke group; it makes no difference how you decide to name the two groups; this decision is up to you.
The null hypothesis states that the population means of the two groups are equal, while the research hypothesis states that the population means of the two groups are not equal. Since you learned how to find the absolute value of t in the previous chapter see Sect. This process was fairly simple once you have had some practice in doing this step. We will discuss that process now.
For our purposes, you can easily understand how to find the degrees of freedom and to use it to find the critical value of t in Appendix E. Take a look at Appendix E.
Instead of using the first column, as we did in the one-group t-test that is based on the sample size, n, of one group of people, we need to use the second column of this table df to find the critical value of t for the two-group t-test. When you go down the second column in Appendix E for the degrees of freedom, you find that once you go beyond the degrees of freedom equal to 39, the critical value of t is always 1. Or: Since the absolute value of t that you found in the t-test formula is greater than the critical value of t in Appendix E, you reject the null hypothesis and accept the research hypothesis.
Writing the conclusion for the two-group t-test is more difficult than writing the conclusion for the one-group t-test because you have to decide what the difference was between the two groups. Suppose that you have been hired as a statistical consultant by Marriott Hotel in St. Louis to analyze the data from a Guest Satisfaction Survey that they give to all customers to determine the degree of satisfaction of these customers for various activities of the hotel.
The survey contains a number of items, but suppose Item 7 is the one in Fig. Louis Marriott Hotel were based on a sample size of men who had a mean score on this item of 6. Suppose that you also had data from 86 women from last week who had a mean score of 6. Louis Marriott Hotel for accepting the null hypothesis degrees of freedom: critical t: t-test formula: Result: Conclusion: 1.
Since the absolute value of 0. There was no difference between male and female guests last week in their rating of the friendliness of the front desk clerk at the St. Louis Marriott Hotel.
Without going into the details of the formulas for the two-group t-test, these data would produce the following result and conclusion based on Fig. Since the absolute value of 5. And, since you rejected the null hypothesis and accepted the research hypothesis, you know that you have found a significant difference between the two mean scores. So, our conclusion needs to contain the following key words: — — — — — — — — — Male guests Female guests Marriott Hotel St.
Louis last week rated the Front Desk Clerks as significantly more friendly than female guests 7. Or: Female guests at the Marriott Hotel in St. Louis last week rated the Front Desk Clerks as significantly less friendly than male guests 4. Both of these conclusions are accurate, so you can decide which one you want to write. It is your choice. Also, note that the mean scores in parentheses at the end of these conclusions must match the sequence of the two groups in your conclusion. Putting the two mean scores at the end of your conclusion saves the reader from having to turn back to the table in your research report to find these mean scores to see how far apart the mean scores were.
Objective: To use Formula 1 for the two-group t-test when both groups have a sample size greater than 30 people 5. You then compared the t-test result to the critical value of t to see if you either accepted the null hypothesis, or rejected the null hypothesis and accepted the research hypothesis. The two-group t-test requires a different formula because you have two groups of people, each with a mean score on some variable.
This formula looks less scary when you break it down into four steps: 1. Square the standard deviation of Group 1, and divide this result by the sample size for Group 1 n1. Square the standard deviation of Group 2, and divide this result by the sample size for Group 2 n2. Add the results of the above two steps to get a total score. Suppose that you have been hired by PepsiCo to do a taste test with teenage boys ages 13—18 to determine if they like the taste of Pepsi the same as the taste of Coke. The boys are not told the brand name of the soft drink that they taste.
Each group rates the taste of their soft drink on a point scale using the following scale in Fig. Note that the two-group t-test does not require that both groups have the same sample size. Your data then produce the following table in Fig.
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Nest, check to see if you have rounded off all figures in D D28 to two decimal places see Fig. Finally, write the following sentence in D36—D38 to summarize the conclusion of the study in plain English: 96 5 Two-Group t-Test of the Difference of the Means for Independent Groups D Teenage boys rated the taste of D Pepsi as significantly better than D the taste of Coke 64 vs.
Save your file as: COKE4 Print this file so that it fits onto one page, and write by hand the null hypothesis and the research hypothesis on your printout. The final spreadsheet appears in Fig. Suppose, further, that you have randomly selected seven wholesalers to purchase the product at the regular price, and they purchased a mean of You want to test to see if the two different prices produced a significant difference in the number of MP3 units sold. You have decided to use the two-group t-test for independent samples, and the following data resulted in Fig.
To do this, click on B at the top left of your spreadsheet to highlight all of the cells in column B. Then, stop clicking! You need three open parentheses and three closed parentheses in this formula or the formula will not work correctly. The above formula gives a standard error of the difference of the means equal to 9.