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... loans available. (Gates, McDaniel; 1999) In our situation this is not the case. In addition, stratification can be time consuming because of the time required to obtain the necessary information. Again this doesnt affect our research because the segmenting information is internal and readily available. Once the means of sampling has been established you can determine the size of the sample by working with management and the designated objectives. (See Appendix Ba for equation and calculation) What this example data is telling us is with a sample size of 89 we can be 95 % confident that the true mean of the quality ratings will be within 5 % of the true population mean. The standard deviation of this equation will have to be estimated.
Usually we would use the results of a pasts study but there is no such study. Another option would be to conduct a pilot study and calculate the standard deviation for those results. In this case we can be extremely positive that any answer will be within 6 standard deviations of the answer. Thus, 6 / 5 = 1. 25 is the equivalent of our standard deviation. Once the sample size is determined we are ready to send the questionnaires out to the customers. Ultimately we want to find average quality ratings for different DTs.
This means that we need to separate or distinguish the questionnaires that come back by their respective DTs. One way to do this is to make a mark on the questionnaire itself. (ie DT = $ 60, 000 gets a red dot; DT = $ 100, 000 gets a yellow dot; DT = $ 120, 000 gets a black dot) This will allow the person receiving the returned questionnaires to separate them by DT and average them separately. Customers will receive the questionnaires on quality via ground mail. Although personal interviews would be preferable, they would not be cost effective or efficient. Instead, the respondents will receive a questionnaire including an envelope that is self-addressed and stamped so that it is easy to return. 89 questionnaires will go out to customers of managers with a DT equal to $ 60, 000. 89 questionnaires will go out to customers of managers with a DT equal to $ 100, 000 and the same for the $ 120, 000 DT level. One of the things that mail surveys always have to deal with is non-response bias.
In a smaller sample, it could drastically affect our results if people do not respond for one reason or another. To minimize this possibility, we will hand stamp and hand address envelopes in order to personalize the exchange. If this doesnt have the desired affect and people dont respond then we will send out a second wave of questionnaires. Initially, we want to test the results of the data we receive for a direct relationship. In other words, we want to make sure that the differences that are apparent between what is observed and what is expected are not due to chance. But rather, we want to be able to show that average quality ratings vary significantly enough with changes in DTs to warrant our continued analysis.
One positive aspect of initially determining whether or not DTs affect quality is that if DTs do not affect quality, we can stop the research and save money and time. This is not as complicated as it sounds, but rather one of the simpler ways to conduct research analysis. The normal way to set up a cross tabulation table is to make a table where the rows (horizontal) consist of categories that influence the data in the columns (vertical). (ie the production targets influence the quality ratings) See Cross tabulation Table in Appendix. Once the table has all the data filled in, percentages can be easily calculated on the basis of row totals.
The results lend themselves to easy comparison of the degree of correlation between DTs and quality ratings. In addition, we will be able to look at a comparison between the observed (O) value and the expected (E) value in each cell. The expected value is representative of the value that would be observed if there was no difference between the variables. (then O = E) The observed value is taken from the data off the questionnaires. The comparison of the observed and the expected is done using a test called Chi Squared or X 2.
The X 2 test enables a research analyst to determine whether an observed pattern of frequencies corresponds to or fits and expected pattern many marketing research studies, possibly most, go no further than cross tabulation in terms of analysis. (Gates, McDaniel; 1999) When conducting a Chi Squared test the first step is to establish the null and alternative hypothesis. In the case of X^ 2, the null hypothesis (Ho) is always an association of no relationship between the two variables (DT and quality). The alternative hypothesis (Ha) is a significant relationship between the two variables. By looking at the answer to the equation, we can compare it to the Chi Square table. From that we determine whether to accept or reject a difference between the two variables.
From the cross tabulation table we can easily apply our data to the X 2 equation. See Figure Bb for equation and calculations. We know the observed value from our data collection. The expected value can be calculated using row sums, column sums and totals. See Figure Bd. And K is equal to the number of categories.
This is all the necessary information to calculate Chi Squared. See Figure Bc. Note: the data that was used was completely fictitious and is used for demonstration purposes only. To calculate the significance of this information two more things are needed.
The first is degrees of freedom and the second is confidence level. With these two pieces of information the results from the Chi Squared test are used to determine a corresponding value from the Chi Squared Table that will relate back to the null hypothesis (Ho). From this information it can be determined if a significant relationship truly does exist between production targets and quality. Degrees of freedom can be calculated from the cross tabulation table by simply subtracting one from both the number of rows and columns and then multiplying the two. (R- 1) (C- 1) = (3 - 1) (5 - 1) = 8 degrees of freedom After that, the researcher would work with management to determine how confident management would want to be in the answer in order to move forward and take action. Because it is better to error on the side of confidence I chose a % 95 confidence level for this example. (industry standard) At these levels the Null Hypothesis exists at 15. 5073 Consequently we can reject the null hypothesis at every level DT because our calculated value is much higher than Ho. (54. 5 vs 15. 5073) From this we conclude that there is a significant difference between quality and DTs. Further analysis of the data will allow us to determine a very close estimate of the exact relationship between DT and quality.
To do this type of extended analysis I would recommend bivariate regression analysis. Although seemingly daunting, this sort of analysis will clearly show the data and the nature of the relationship in such a way as to permit the management to determine where to set production targets in order to achieve desired levels of quality. We use bivariate regression analysis to determine the strength of the linear relationship between two variables when one is considered dependent (y) and the other independent (x). (Gates, McDaniel; 1999) In this research, the DT is the independent (x) variable while the quality is the dependent (y) variable. Interpreting the graph of the bivariate regression analysis is not difficult.
There is an obvious inverse or negative relationship. This means that as one variable increases the other decreases. The benefit of such an analysis to the management is our ability to extrapolate that data. By taking a straight line graph and making a best fit line through the data points you can look at a DT and immediately get a sense of what sort of quality to expect from your managers.
Finally, I feel I have demonstrated that the objectives laid before you in this proposal are reachable and actionable. The insight that this sort of research could provide xxx management would be unparalleled. It could provide tremendous leverage for maintaining and strengthening your customer base into the next millenium. The overall quality of the work was high. 1) strongly disagree 2) disagree 3) neutral 4) agree 5) strongly agree 1) strongly disagree 2) disagree 3) neutral 4) agree 5) strongly agree The workers were conscientious about your concerns. 1) strongly disagree 2) disagree 3) neutral 4) agree 5) strongly agree The work was done in a timely fashion. 1) strongly disagree 2) disagree 3) neutral 4) agree 5) strongly agree The workers paid attention to detail. 1) strongly disagree 2) disagree 3) neutral 4) agree 5) strongly agree 1) strongly disagree 2) disagree 3) neutral 4) agree 5) strongly agree The manager kept the lines of communication open. 1) strongly disagree 2) disagree 3) neutral 4) agree 5) strongly agree The manager delivered on what was promised. 1) strongly disagree 2) disagree 3) neutral 4) agree 5) strongly agree I am likely to recommend College Pro Painters to friends and family. 1) strongly disagree 2) disagree 3) neutral 4) agree 5) strongly agree xxxi's one of many different companies that operate under The Franchise Company. xxx has been around since the late seventies when it began in Canada.
Now it is mainly in the U. S. where it operates in over 20 states. The basic premise behind xxx is a company that hires and trains college students to run their own businesses. These businesses are called franchises but unlike many franchises, the student manager / franchisee does not have to buy the franchise. Rather, he or she pays royalty on every job produced.
After a intense interviewing season in the Fall the new managers go through a rigorous training period where they are taught everything from selling to production and all the comes in between. During the Spring months the managers are expected to book the majority of the work they will be doing over the summer. As the summer approaches, they begin to focus on hiring workers (also college students) and training them. Once the summer begins managers are exposed to everything a young businessman could hope to experience and many other things they hoped not to experience. In general, it is a very tight ship. xxx general managers (2 in Washington) are responsible for hiring the managers they will stick with throughout the year.
For this reason, GMs have weekly checkpoints with their managers counseling and guiding them through the stressful summer. Each General Manager is responsible for about 15 - 20 managers. In an average summer an average manager will paint about 20 homes. This works out to roughly 400 customers per GM and 800 per state. Graphs of the inverse relationship between quality and production targets x-axis is quality rating scale (5 is high) y-axis is total quality rating points a) The formula for calculating the required sample size for problems that involve the estimation of a mean is (Gates, McDaniel; 1999): Sample size (N) equals level of confidence (Z) squared times standard deviation (o) squared all divided by the acceptable amount of sampling error (E) squared.
b) The equation for the Chi Squared test is as follows: c) Chi Squared Calculations (from cross tabulation table) At a DT of $ 60, 0015) 2 + (14 - 26. 3) 2 + (29 - 20. 6) 2 + (38 - 20) 2 = 33. 5 7. 3 15 26. 3 20. 6 20 At a DT of $ 100, 0018 - 15) 2 + (33 - 26. 3) 2 + (18 - 20. 6) 2 + (12 - 215 26. 3 20. 6 20 At a DT of $ 120, 000 X 2 = (11 - 7. 3) 2 + (22 - 15) 2 + (32 - 27) 2 + (15 - 20. 6) 2 + (9 - 20) 2 = 15. 3 7. 3 15 26. 3 20. 6 20 Degrees of Freedom = (R- 1) (C- 1) = (3 - 1) (5 - 1) = 8 REJECT NULL HYPOTHESIS AT EVERY LEVEL OF PRODUCTION TARGET d) The calculation for determining E for any given cell is as follows: E = (Csum) x (Cum) x total = (Csum) (Cum) total total total Brown, Timothy P. (1991), Internal research helps to define service quality; Marketing News, Feb. 4 1991 v 25 n 3 p 11 (1). Dickson, J. P. (1999), BPA 402: Business Research; Personal Communication. Gates and McDaniel (1999), Contemporary Marketing Research.
Cincinnati: South-Western College Publishing. Gitlow, Howard S. (1990), Planning for quality Productivity and Competitive Position. Homewood, Ill. : Dow Jones-Irwin. Law, Patricia (1980), Advance Questionnaire Design.
Cambridge, Mass. : Abt Books. Bibliography:
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