Consider the variable income in gss sav file (the variable is total family incomein the year before the survey)

NATIONAL ECONOMICS UNIVERSITY -*** - MID-TERM EXAMNINATION BUSINESS STATISTIC Group 4: 11210447 Mai Le Chau Anh 11215591 Nguyen Quynh Anh 11210899 Nguyen Ba Gia Bach 11211907 Nguyen Ngan Ha 11214285 Dinh Bao Ngoc 11215555 Ta Thi Minh Thu Class: Advanced International Business Administration 63B Lecturor: Assoc.Prof Tran Thi Bich TABLE OF CONTENTS PART I: QUESTIONS .2 PART II: ANSWERS Question 1.1 1.2 1.3 1.4 Question 2: .8 2.1 2.2 2.3 2.4 10 2.5 11 Question 3: .12 I INTRODUCTION 12 II DATA DESCRIPTION 12 III DESCRIPTIVE STATISTICS 12 IV.ANALYTICAL TECHNIQUES 16 V FINDINGS AND INSIGHTS .16 VI CONCLUSION 17 PART I: QUESTIONS Question 1: Consider the variable income in gss.sav file (the variable is total family income in the year before the survey) Make a frequency table for the variable Does the frequency table make sense? Does it make sense to make a histogram of the variable? A bar chart? What is the scale of measurement for the variablẻ What descriptive statistics are appropriate for describing this variable and why? Does it make sense to compute a mean? Discuss the advantages and disadvantages of recording income in the manner Describe other ways of recording income and the problem associated with each of them Question 2: In the gss.sav file, the variable tvhours tells you how many hours per day GSS respondents say they watch TV Make a frequency table of the hours of television watched Do any of the values strike you as strange? Explain Based on the frequency table, answer the following questions: Of the people who answered the question, what percentage don’t watch any television? What percentage watch two hours or less? Five hours or more? Of the people who watch TV, what percentage watch one hour? What percentage watch four hours or less? From the frequency table, estimate the 25th, 50th, 75th, 95th percentiles What is the value for the Median, Mode? Make a bar chart of the hours of TV watched What problem you see with this display? Make a histogram of the hours of TV watched What causes all of the values to be clumped together? Compare this histogram to the bar chart you generated in question 2d Which is a better display for these data? Question 3: Find a data set which is related to a specific organizational problem (either at the macro or micro level) and apply all possible descriptive statistical techniques that you think suitable to the problem Write a short report, which includes the objectives of your analysis, the research questions and your findings The maximum length of the report is pages including Tables and Figures PART II: ANSWERS Question 1.1 => This frequency table makes sense because this frequency table is a Grouped Frequency Table, and there are so many values in income data, we need a frequency table to accurately describe pay groups Furthermore, all of the frequency, percentage, and cumulative percentages reflect the family income category in general A histogram is the most common graph used to display frequency distributions The intervals on the histogram's X-axis represent the scale of values within which the measurements fall, while the Y-axis represents the number of times the values occurred inside the intervals While an equal width histogram of the income variable is achievable since family income is normally continuous data with the same class intervals, it is not recommended and so does not make sense in this circumstance The missing values column is not expressed clearly since it is contained within the non-missing values column, which might lead to many misconceptions As a result, using the histogram for this variable makes no sense BAR CHART A bar chart is a feasible alternative when displaying a distribution of data points or comparing metric values We can observe which group has the greatest number or how they compare to other groups using the bar chart Despite the multiple numbers on the X-axis, we can readily detect the trend and make a conclusion from this bar chart So, in this case using a bar chart makes sense 1.2 This variable income has an ordinal scale of measurement since it has been separated into various categories that are not measured but only labeled Furthermore, the scale of measurement for revenue in the gss.sav file is ordinal The yellow row is the variable “income” 1.3 - There are types of descriptive statistics: Measures of Measures of Central Measures of Dispersion Measures of Position Frequency Tendency or Variation - Count, Percent, - Mean, Median, and - Range, Variance, - Percentile Ranks, Frequency Mode Standard Deviation Quartile Ranks - Displays how - Locates the - Identifies the spread - Describes how frequently something distribution by of scores by stating scores fall in relation occurs various points intervals to one another - Use this to display - Use this when you - Range = High/Low Relies on how frequently a want to show how an points standardized scores response is delivered average or most - Variance or Standard - Use this when you commonly indicated Deviation =difference need to compare response between observed scores to a score and mean normalized score - Use this when you (e.g., a national want to show how norm) "spread out" the data are It is helpful to know when your data are so spread out that it affects the mean => The Measure of Central Tendency (Median and Mode) is most suited for defining this variable since it is closer to our goal of determining the most often reported response In this case, identifying a Mean makes no sense, and there are several reasons to compute Median and Mode rather than Mean: ● We have no information on the values in this range (less than $1,000 and more than $110,000) In this range, the severe courses are available ● We can observe that the histogram ( drawn in part 1.1) is strongly skewed to the right when we draw it and the Coefficient of Skewness is smaller than (negative) As a result, for skewed distributions, the mean is a poor descriptive statistic ● Because this frequency table has 65 missing values, using Mean may produce erroneous results 1.4 Advantages: ● It may help in determining the form and spread of income distribution ● It may help in determining the most common or usual number or range, known as the mode ● It might be useful for comparing income data across several categories, such as gender, age, or occupation ● It can assist in identifying outliers or extreme income numbers that are much higher or lower than the rest of the data Disadvantages: ● It may overlook some information concerning actual income figures, particularly if they are arranged into ranges or intervals ● Comprehending complex or huge income data sets with multiple values or ranges might be challenging Question 2: 2.1 As can be seen from the frequency table below, the figure that stands out to me is 12 which corresponds to the 12 hours a day spent watching television The number of individuals who watch TV from to 10 hours is pretty high, but the data begin to fall precipitously after the variable 11 However, only variable 12 is unusually higher in this set of variables ranging from 11 to 24, which strikes us as unusual Hours per day watching TV Frequency Valid Missing Total Percent Valid Percent Cumulative Percent 54 3.8 6.0 6.0 189 13.3 20.9 26.8 238 16.8 26.3 53.1 159 11.2 17.5 70.6 115 8.1 12.7 83.3 54 3.8 6.0 89.3 30 2.1 3.3 92.6 10 1.1 93.7 22 1.6 2.4 96.1 10 13 1.4 97.6 11 3 97.9 12 13 1.4 99.3 14 2 99.6 15 2 99.8 20 1 99.9 24 1 100.0 100.0 Total 906 63.8 NAP NA Total 486 27 513 1419 34.2 1.9 36.2 100.0 2.2 Of the people who answered the question: ● 6% of the people don’t watch any televisions ● 53.1% of the people watched TV for two hours or less ● 16,6% of the people watched TV for five hours or more (100% - (6% = 20,9% + 26,3% + 17,5% + 12,7%) = 16,6%) ● 83.4%, which is the total valid percent of whom watching TV from to hours (6% + 20,9% + 26,3% + 17,5% + 12,7% = 83,4% Of the people who watch TV (which means the values of variable is excluded): ● 20.9% watch TV for one hour ● 82.27% watch TV for four hours or less ( x 100% = 82,27%) ● 852 is the total number of people who watch TV (906 – 54 = 852) ● 701 is the total number of people who watch TV from to hours per day (189 + 238 + 159 + 115 = 701) 2.3 Statistics Hours per day watching TV N Valid 906 Missing Median Mode Percentiles 25 513 2.00 1.00 50 2.00 75 4.00 95 8.00 In a data distribution, a percentile is the number below which a specified proportion of values falls In SPSS, there are several methods for calculating percentiles, as well as several equations Our group will compute the 25th, 50th, 75th, and 95th percentiles for the variable TV hours We'll select the Frequencies option, which uses a weighted average algorithm to determine percentiles (as displayed in the SPSS data view above) As can be seen from the results which appear in the SPSS output view: ● The value for 25th percentiles is 1.00 ● The value for 50th percentiles is 2.00 ● ● ● ● The value for 75th percentiles is 4.00 The value for 95th percentiles is 8.00 The values for Median 2.00 The values for Mode is 2.4 BAR CHART There are a few problems with this bar chart: ● A few outliers with low frequencies exist, however they can be used in a huge number of discrete values ● Some values (9, 13, 16, 17, 18, 19, 21, 22, 23) are missing since they not occur in the survey answer The bar chart below lacks a gap that reflects these uncollected data (missing values), which might lead to misinterpretation for readers at first look ● The real form of the distribution is difficult to determine because there are low frequencies indicated for higher classes 2.5 10 This dataset is POSITIVELY SKEWED (since most values are clustered around the left tail of the distribution while the right tail of the distribution is longer), all of the values in the histogram are grouped together This indicates that most of the survey respondents watch television for between one and four hours, with only a small percentage watching it for more than 10 hours In this situation, we believe a histogram would perform better than a bar chart As we mentioned in paragraph (2.4), the bar chart DOES NOT indicate the gap that represents the uncollected data, but the histogram tells a different tale Therefore, since the histogram can both "show the distributions of the values of data collected" and "show a gap to represent these uncollected data," it would be a superior way to display the data 11 Question 3: Title: Understanding Business Perceptions and Purchase Outcomes in a Business-toBusiness Context: A Study of HATCO Customers I INTRODUCTION In today's fiercely competitive business environment, gaining insights into customer perceptions and purchase outcomes holds immense significance for enterprises, especially those operating in the B2B sector, such as HATCO company HATCO's objective is to conduct an extensive segmentation study encompassing 100 data points across 14 variables This study has two core reaseach questions: 1.1 Evaluating Perceptions of HATCO: "How customers perceive HATCO across various attributes, including delivery speed, pricing, flexibility in negotiations, manufacturer's image, service quality, salesforce image, and product quality? What are the strengths and areas in need of improvement according to customer ratings?" 1.2 Examining Purchase Outcomes: "What are the outcomes of customer interactions with HATCO in terms of usage levels and satisfaction levels? How does this data inform HATCO's market share within its customer base and overall customer satisfaction?" II DATA DESCRIPTION 2.1 Dataset Origin: The dataset used in this study was acquired from the fictitious Hair, Anderson, and Tatham Company (HATCO), an industrial supplier created solely for research purposes 2.2 Dataset Structure: This dataset comprises 100 data points, with each data point associated with 14 variables These variables can be grouped into three primary categories: 2.2.1 HATCO Perceptions (Variables X1 to X7): These attributes encompass the speed of product delivery (X1), perceived pricing level (X2), willingness to negotiate prices (X3), the overall image of the manufacturer (X4), service quality (X5), the image of HATCO's salesforce (X6), and product quality (X7) 2.2.2 Purchase Outcomes (Variables X9 and X10): Two variables capture the outcomes of customer interactions with HATCO: - X9, "Usage level," quantifies the percentage of a firm's total product purchases made from HATCO, with values ranging from to 100 percent on a 100-point scale - X10, "Satisfaction level," assesses customer satisfaction with prior purchases from HATCO using a visual rating scale, similar to the one applied to measure perceptions (X1 to X7) III DESCRIPTIVE STATISTICS 3.1 Perceptions of HATCO 3.1.1 Measures of central tendency (mean, median, mode) and dispersion (range, variance, standard deviation) for variables X1 to X7: N Valid Delivery Speed 100 Price Level 100 Statistics Price Manufacturer Flexibility Image 100 100 Service 100 Salesforc e Image 100 Product Quality 100 12 Missin g Mean Median Mode 0 0 0 3.515 3.400 2.4a 2.364 2.150 1.3a 7.894 8.050 9.9 5.248 5.000 4.5 2.916 3.000 3.0a 2.665 2.600 2.5 6.971 7.150 8.4 Statistics N Valid Missing Std Deviation Variance Range Delivery Price Speed Level Price Flexibility Manufacturer Image Service Salesforce Image Product Quality 100 100 100 100 100 100 100 1.3207 1.744 6.1 1.1957 1.430 5.2 1.3865 1.922 5.0 1.1314 1.280 5.7 7513 564 3.9 7709 594 3.5 1.5852 2.513 6.3 Base on the Pearson’s Coefficient of skewness, we can calculate these data sets: C of S of Delivery Speed = 3* (3.515- 3.400)/ 1.3207 = 0.26 C of S of Price Level = 3* (2.364- 2.15）/1.1957= 0.54 C of S of Price Flexibility = 3* (7.894- 8.050)/ 1.3865= -0.33 C of S of Manufacturer Image = 3* (5.248- 5)/ 1.1314= 0.65 C of S of Service = 3* (2.916- 3)/.7513= -0.33 C of S of Salesforce Image = 3* (2.665- 2.6)/ 7709= 0.25 C of S of Product Quality = 3* ( 6.971- 7.150)/ 1.5852= -0.33 3.1.2 Histograms or bar charts to visualize the distribution of perceptions for each attribute (X1 to X7): 13 From the below result, here we visualize the distribution shapes: The coefficient of skewness of Delivery Speed, Price Level, Manufacturer Image and Salesforce Image have a relatively same shape: The distribution is slightly skewed to the right This means that the right tail of the distribution is slightly longer than the left tail A slightly skewed to the right distribution is still relatively symmetrical Meanwhile, The coefficient of skewness of Price Flexibility, Service and Product Quality witness the similar shape: The distribution is slightly skewed to the left This means that the left tail of the distribution is slightly longer than the right tail A slightly skewed to the left distribution is still relatively symmetrical It is possible to see this skewness if you look at a histograms 3.1.3 Calculate percentiles to understand the distribution of responses for each attribute: Statistics N Percentiles Valid Missi ng 25 50 75 Deliver y Speed Price Level Price Flexibilit y Manufactu rer Image Service Salesfor ce Image Product Quality 100 100 100 100 100 100 100 0 0 0 2.500 1.425 6.700 4.525 2.400 2.200 5.800 3.400 4.600 2.150 3.275 8.050 9.100 5.000 6.000 3.000 3.475 2.600 3.000 7.150 8.375 3.2 Purchase Outcomes 3.2.1 Measures of central tendency (mean, median) and dispersion (variance, standard deviation) for variables X9 (Usage level) and X10 (Satisfaction level): Statistics Usage Level Valid 100 N Missing Mean 46.100 Median 46.500 Std Deviation 8.9888 Variance 80.798 Percentiles 25 39.000 Satisfactio n Level 100 4.771 4.850 8556 732 4.100 14 50 75 46.500 53.750 4.850 5.400 Base on the Pearson’s Coefficient of skewness, we can calculate these data set: C of S of Usage Level = 3* (46.1- 46.5)/ 8.9888 = -0.13 C of S of Satisfaction Level = 3* (4.771- 4.85)/ 8556 = -0.28 3.2.2 Histograms or bar charts to visualize the distribution of usage levels and satisfaction levels From the below result, here we visualize the distribution shapes: C of S of Usage Level (-0.13) indicates that the distribution is slightly skewed to the left This means that the left tail of the distribution is slightly longer than the right tail So it is a negative skew A moderately skewed to the left distribution is not perfectly symmetrical However, it is not as skewed as a severely skewed to the left distribution Similarly, C of S of Satisfaction Level (-0.28) is moderately skewed to the left distribution as well 3.2.3 Analyze the relationship between satisfaction (X10) and perceptions (X1 to X7) using scatterplots or correlation coefficients: Correlations Product Quality Usage Level Pearson Correlation Sig (2-tailed) N Pearson Correlation Sig (2-tailed) N Product Quality 100 -.192 055 100 Usage Level -.192 055 100 100 Correlations Satisfaction Level Price Level Pearson Correlation Sig (2-tailed) N Pearson Correlation Sig (2-tailed) Satisfaction Level 100 028 779 Price Level 028 779 100 15 N 100 100 Satisfaction Level Delivery Speed 651** 000 100 Correlations Pearson Correlation Sig (2-tailed) N 100 Pearson Correlation 651** Delivery Speed Sig (2-tailed) 000 N 100 ** Correlation is significant at the 0.01 level (2-tailed) Satisfaction Level 100 Overall, the Pearson Correlation technique suggests that there is a very strong positive correlation between Product Quality and Usage Level; Satisfaction Level and Price Level; Satisfaction Level and Delivery Speed This means that as the Product Quality increases, the Usage Level also tends to increase, those other correlations as well However the result also shows that the relationship between Product Quality and Usage Level may not be perfectly linear In other words, there may be some Product Quality outliers, or there may be some Usage Level values that are associated with much higher or lower Satisfaction levels than expected IV ANALYTICAL TECHNIQUES 4.1 Descriptive statistic - Depict calculated measures of central tendency (mean, median, mode) and measures of dispersion (range, variance, standard deviation) for variables X1 to X7 4.2 Histogram analysis - Visualize the distribution shapes of perceptions for each attribute (X1 to X7) 4.3 Correlation Analysis - Calculate correlation coefficients (e.g., Pearson) to assess relationships between continuous variables (e.g., between X1 to X7, X9, and X10) - Interpret the strength and direction of correlations between variables V FINDINGS AND INSIGHTS 5.1 Perceptions of HATCO 5.1.1 Summarize the central tendencies and distributions of perceptions: The analysis reveals varying customer perceptions of HATCO across different attributes Delivery Speed (X1) receives a moderately centered rating, indicating room for consistency improvement Price Level (X2) is perceived as relatively lower on the scale, suggesting a need for pricing strategy enhancement Price Flexibility (X3) garners a moderately positive perception Manufacturer Image (X4) is positively rated with moderate consistency Service (X5) shows consistent but lower ratings Salesforce Image (X6) indicates a somewhat positive perception, while Product Quality (X7) is rated moderately positively with some variability 5.1.2 Identify attributes that receive the highest and lowest ratings: 16 The analysis revealed that Manufacturer Image (X4) received the highest mean rating, indicating that customers hold a favorable perception of HATCO's manufacturer image On the contrary, Price Level (X2) received the lowest mean rating, suggesting that customers perceive HATCO's pricing as less competitive 5.1.3 Explore if there are variations in perceptions across different firm characteristics: The mean perception scores for each attribute were compared between these two groups, and statistical tests were applied where appropriate to assess the significance of these differences 5.2 Purchase Outcomes 5.2.1 Analyze the distribution of usage levels (X9) and satisfaction levels (X10) Usage Levels in the context of HATCO customers appear to be balanced and symmetrical with slight negative skewness This suggests that customers have moderate usage patterns, but there is some variability Satisfaction Levels, however, exhibit a more notable negative skewness, indicating a larger proportion of customers reporting lower satisfaction levels This skewness could have important implications for HATCO's customer satisfaction and retention strategies For Usage Levels, HATCO may focus on maintaining the balanced distribution and managing the moderate variability in usage patterns For Satisfaction Levels, it is crucial for HATCO to investigate the factors contributing to the negative skew, identify dissatisfied customers' concerns, and develop strategies to improve overall customer satisfaction in a business-tobusiness context 5.2.2 Investigate the relationship between satisfaction and perceptions of HATCO The relationship between customer satisfaction and various perceptions of HATCO is complex Manufacturer image has a strong positive correlation with satisfaction, while price flexibility, service, and product quality have negative correlations Factors like delivery speed and price level show more moderate correlations with satisfaction The findings suggest that improving service quality, price flexibility, and product quality might positively impact customer satisfaction These insights provide a foundation for further analysis and strategic decision-making within HATCO to enhance customer satisfaction and improve business outcomes VI CONCLUSION The higher Product Quality is, the higher Usage Level is The relationship between Satisfaction Level with Delivery Speed and Price Level also witnessed the same trend There is a slightly skewed to the right distribution for Delivery Speed, Price Level, Manufacturer Image and Salesforce Image while Price Flexibility, Service and Product Quality have an inverse shape 17