Managing Information Statistical Significance - Assignment Example

ASSIGNMENT PRO FORMA NUMBER (this does not start with two letters, that is your e-mail number) SHEET NUMBER (the number of the sheet which contained the data) Task(a) – Group Spending British German French Italian Mean 427.19 435.94 408.88 451.12 Sample Standard Deviation 135.87 106.37 128.52 138.79 Standard Error 19.61 15.04 18.18 19.25 Estimate of Mean X X X X Upper Limit 465.62 465.42 444.50 488.84 Lower Limit 388.75 406.46 373.26 413.39 Comment on the statistical significance. The mean identifies the central tendency of the samples while the standard deviation illustrates the spread of the samples from the mean. The survey results show that the mean spending for the different nationalities ranges from 408 to 451. On the surface this range might be considered close, however the large standard deviations within each group might call for better sampling or further research if the survey is to be more conclusive, e.g. when we factor in the standard error, the range enlarges from 408 - 451 to 388 – 488. The way forwards would probably be to conduct a survey that shall have less standard deviations. A quick way would be to increase the sample size. Comment on the usefulness in developing a marketing plan. The keyword here is market segmentation. From the above data analysis Andreas Papodopolous can get an idea as to which groups spend more such that they could be targeted with better tourist packages. For example we can observe that Italian groups, in spite of the higher standard deviation have the highest spending limits (upper and lower), while French groups spend the least. Additionally, we can observe that German groups have the least variability in terms of spending thus targeting them with certain spend packages will more likely yield success than for the other groups. Task(b) – Individual Spending British German French Italian Mean 132.09 132.03 121.45 137.95 Sample Standard Deviation 37.55 30.63 43.12 41.77 Standard Error 5.42 4.33 6.10 5.79 Estimate of Mean X X X X Upper Limit 142.71 140.52 133.40 149.30 Lower Limit 121.47 123.55 109.49 126.60 Comment on the statistical significance. The individual spending analysis gives us a clearer picture on the individual contributions of each nationality. It corroborates the results of the group spending especially with regards to showing which country’s individuals spend more on average. We see the Italians topping and the French tailing. The standard error here is much lower than for the group spending data which means that these results have a higher accuracy and should probably be used instead of the group spending data. Comment on the usefulness in developing a marketing plan. Considering that these results have lower standard deviations in comparison to the group spending data, Andreas Papodopolous would be better able to develop tourist packages focused on the different nationalities based on this. Task(c) – Difference in Means of Group Spending Standard Error British German French Italian British X 24.71 26.74 27.48 German 24.71 X 23.59 24.43 French 26.74 23.59 X 26.48 Italian 27.48 24.43 26.48 X Z-score British German French Italian British X 0.35 -0.68 0.87 German -0.35 X -1.15 0.62 French 0.68 1.15 X 1.60 Italian -0.87 -0.62 -1.60 X Comment on the statistical significance. The difference in means identifies the relation of one group of independent sample from another. The standard error estimates the deviation of sampling distribution from one nationality to the other. This shows how much fluctuation of samples in the survey results. On the other hand, the z-score estimates how many standard deviations is the estimate above or below the mean. Results from this survey demonstrate that standard error difference between group spending is large. This implies that the survey requires more samples in order for us to obtain better relationship estimates. However, when we factor in the z-score, we observe that z-scores are below 2. From this we can conclude with 95% certainty that all the groups come from the same population. Comment on the usefulness in developing a marketing plan. A marketing plan considers the different behaviors of consumer groups. The conclusions from the Z-scores would inform Andreas Papodopolous that this data is representative of the tourist population that visits their town, thus developing a marketing strategy based on this data will not be far from reality. Task(d) – Difference in Means of Individual Spending Standard Error British German French Italian British X 6.94 8.16 7.93 German 6.94 X 7.48 7.23 French 8.16 7.48 X 8.41 Italian 7.93 7.23 8.41 X Z-score British German French Italian British X -0.01 -1.30 0.74 German 0.01 X -1.41 0.82 French 1.30 1.41 X 1.96 Italian -0.74 -0.82 -1.96 X Comment on the statistical significance. The difference in means of individual spending shows that the relationship from one nationality to the other is close as shown by the small value of the standard error. Surprisingly, the z-scores of individual spending are larger than that of group spending. Nevertheless the Z-scores still lie below 2 and this supports the conclusion we made with the group spending i.e. all individuals surveyed belong in the same population. Comment on the usefulness in developing a marketing plan. The fact that Z-scores give us a 95% certainty that the individuals sampled belong to the same population should encourage Papodopolous to have faith in this data and therefore focus on developing an appropriate marketing strategy. Task(e) - Regression British German French Italian Intercept 155.47 173.23 142.36 205.50 Slope 77.17 74.63 70.88 66.52 Comment on the statistical significance. A positive slope implies an increase in amount spent per corresponding increase in individuals in a group. The greater the slope the more the increase in expenditure as group size increases. Intercept shows us the minimum amount that can be spent per group size. Comment on the usefulness in developing a marketing plan. When looking at the above data Andreas Papodopolous would quickly notice that Italian groups spend more than any other group when they are few but as their group size increases the corresponding increase in amount spent is the least. On the other hand, the British have the greatest slope which implies that they spend the most per increase in group size. In developing a market plan therefore, Papodopolous, could target tourist packages for small sized Italian groups and large British groups so as to maximize on his city’s income. Task(f) - Correlation British German French Italian R2 coefficient 0.78 0.81 0.80 0.73 Standard Error of intercept 23.06 19.61 20.82 23.16 Standard Error of slope 6.00 5.24 5.09 5.66 T statistic of intercept 6.74 8.83 6.84 8.87 T statistic of slope 12.86 14.24 13.92 11.76 Comment on the statistical significance. R2 coefficient provides a measure of goodness-of-fit of linear regression. Results show that the Germans and French have the closest linear regression in addition to low standard errors. The T-statistics show that all variables here are independent from each other. Comment on the usefulness in developing a marketing plan. The R2 coefficient is not quite linear, the highest is 0.81, therefore Papodopolous should probably not take this that there is a linear relationship between the group size and amount spent there could be other factors at play. However, he could take the low standard error in the German and French groups to take it that spending behavior is not widely spread within these groups with respect to the mean spending. Task(g) – Estimate for the spending of a family of 2 adult and 4 children. British German French Italian Estimate 618.49 621.01 567.64 604.62 Comment on the statistical significance. When we assume that a group is comprised of 2 adults and 4 children, we can estimate their spending using the assumption of a straight line equation y=mx + c, where m is the regression slope and c is the intercept. Comment on the usefulness in developing a marketing plan. The whole idea behind obtaining a regression is to evaluate the relationship between number of individuals in a group and the amount spent. The more accurate the relationship Andreas Papodopolous obtains between his variable , the more accurately he will be able to predict on group sizes and spend per nationality which will enable him to mass customize tourist packages that will give his city the best returns. Task(h) – Difference of opinions within nationalities British German French Italian Chi-square value 5.62 18.39 6.38 10.46 Comment on the statistical significance. The chi-square value approximates the significance of two or more independent variables with defined degrees of freedom. In this case, the variables are the opinions of each nationality with 9 degrees of freedom. The results show that the Germans have a greater difference in opinions as compared to the other nationalities, while the British have more or less similar opinions. Comment on the usefulness in developing a marketing plan. The marketing plan is effective if it considers the opinions of the people surveyed. It can be deduced that the British and French have similar opinions within the groups while the German have diverse opinions. The marketing plan can focus on the opinion of the British and French because it has a significant probability that an individual opinion belonging to the group is similar to the others in the group. Task(i) – Difference of opinions between nationalities Overall Accommodation Location Food Chi-square value 30.00 19.55 38.72 27.40 Comment on the statistical significance. The difference of opinions between nationalities is diverse when considering specific criteria. The chi-square value of the overall opinion, for example, is large such that there is no conclusive evidence that each nationality has similar opinions. The chi-square value that is large does not guarantee a relationship. Comment on the usefulness in developing a marketing plan. With the results of the difference of opinions between nationalities, it can be assessed that every nationality has varying opinion and preference. Thus, the marketing plan cannot consider the whole population as one when being marketed but instead consider every nationality as different from the other. Task(j) – Difference in Proportions of Positive Opinions of the Accommodation. Standard Error British German French Italian British X 0.0968 0.0982 0.0973 German 0.0968 X 0.0974 0.0964 French 0.0982 0.0974 X 0.0978 Italian 0.0973 0.0964 0.0978 X Z-score British German French Italian British X 2.9523 2.3004 2.2904 German 2.9523 X -0.6162 -0.6540 French -2.3004 0.6162 X -0.0315 Italian -2.2904 0.6540 0.0315 X Comment on the statistical significance. The probability that the each nationality has similar positive opinion on accommodation is very small. The z-score of the between nationality is large such that there a very small probability that two nationalities have the same opinion. With the exception of the French and Italian, other nationalities have no relationship on their opinion. Comment on the usefulness in developing a marketing plan. When considering the relationship of consumer taste and preference between two groups, the marketing plan considers the variation or distribution of such taste and preference. As with the results, only the French and Italians have similar taste and preferences on the accommodations. Task(j) – Difference in Proportions of Positive Opinions of the Food. Standard Error British German French Italian British X 0.0963 0.0973 0.0950 German 0.0963 X 0.0990 0.0967 French 0.0973 0.0990 X 0.0977 Italian 0.0950 0.0967 0.0977 X Z-score British German French Italian British X 2.9851 1.7214 3.1878 German 2.9851 X -1.2127 0.1591 French -1.7214 1.2127 X 1.3858 Italian -3.1878 -0.1591 -1.3858 X Comment on the statistical significance. The z-score is large between the differences of positive opinions of the food among nationalities. This means that there is a small probability that one nationality would have the same opinion from another. Except for the Italian and German, the preference of other nationalities on the food is different and varied. Comment on the usefulness in developing a marketing plan. When marketing the food, the German and Italian have similar taste and preference, while the rest have dissimilar opinions. This means that the marketing plan that considers the food should consider the German and Italian as similar while the rest as different. Therefore, the marketing plan on food is diverse. Section Two Task(a) – Group Spending Mean =AVERAGE(E178:E229) Standard deviation =STDEV(E178:E229) Standard error =(STDEV(E178:E229))/(SQRT(COUNT(E178:E229))) 95% Confidence Interval (CI)= CONFIDENCE(0.05,E232,COUNT(E178:E229)) Upper limit = Mean + CI Lower limit = Mean - CI Task(b) – Individual Spending Similar to Task (a)after dividing Group spend by number of individuals. Task(c) – Difference in Means of Group Spending Standard Error y (differences) = Square Root {(SE Group x)2 + (SE Group y)2} Z-Score y(differences)= (Mean Group x - Mean Group y)/ Standard Error Group y(diff) Task(d) – Difference in Means of Individual Spending Similar to Task (c)but using data for individual spending Task(f) - Correlation =LINEST(y,x,1,1) Slope Intercept Standard Error in slope Standard Error in intercept R2 Standard Error in a calculated y Task(g) – Estimate for the spending of a family of 2 adult and 4 children. Y= mx + C ; x= slope, C = y intercept A family of 2 adult + 4 children = group of 6 Therefore our x= 6 For Germans y = 74.63x + 173.23 = 74.63 (6) + 173.23 = 621.01 Task(h) – Difference of opinions within nationalities Read More

However, when we factor in the z-score, we observe that z-scores are below 2. From this we can conclude with 95% certainty that all the groups come from the same population. Comment on the usefulness in developing a marketing plan. A marketing plan considers the different behaviors of consumer groups. The conclusions from the Z-scores would inform Andreas Papodopolous that this data is representative of the tourist population that visits their town, thus developing a marketing strategy based on this data will not be far from reality. Task(d) – Difference in Means of Individual Spending Standard Error British German French Italian British X 6.94 8.16 7.

93 German 6.94 X 7.48 7.23 French 8.16 7.48 X 8.41 Italian 7.93 7.23 8.41 X Z-score British German French Italian British X -0.01 -1.30 0.74 German 0.01 X -1.41 0.82 French 1.30 1.41 X 1.96 Italian -0.74 -0.82 -1.96 X Comment on the statistical significance. The difference in means of individual spending shows that the relationship from one nationality to the other is close as shown by the small value of the standard error. Surprisingly, the z-scores of individual spending are larger than that of group spending.

Nevertheless the Z-scores still lie below 2 and this supports the conclusion we made with the group spending i.e. all individuals surveyed belong in the same population. Comment on the usefulness in developing a marketing plan. The fact that Z-scores give us a 95% certainty that the individuals sampled belong to the same population should encourage Papodopolous to have faith in this data and therefore focus on developing an appropriate marketing strategy. Task(e) - Regression British German French Italian Intercept 155.47 173.23 142.36 205.50 Slope 77.17 74.63 70.88 66.52 Comment on the statistical significance.

A positive slope implies an increase in amount spent per corresponding increase in individuals in a group. The greater the slope the more the increase in expenditure as group size increases. Intercept shows us the minimum amount that can be spent per group size. Comment on the usefulness in developing a marketing plan. When looking at the above data Andreas Papodopolous would quickly notice that Italian groups spend more than any other group when they are few but as their group size increases the corresponding increase in amount spent is the least.

On the other hand, the British have the greatest slope which implies that they spend the most per increase in group size. In developing a market plan therefore, Papodopolous, could target tourist packages for small sized Italian groups and large British groups so as to maximize on his city’s income. Task(f) - Correlation British German French Italian R2 coefficient 0.78 0.81 0.80 0.73 Standard Error of intercept 23.06 19.61 20.82 23.16 Standard Error of slope 6.00 5.24 5.09 5.66 T statistic of intercept 6.74 8.83 6.84 8.87 T statistic of slope 12.86 14.24 13.92 11.76 Comment on the statistical significance.

R2 coefficient provides a measure of goodness-of-fit of linear regression. Results show that the Germans and French have the closest linear regression in addition to low standard errors. The T-statistics show that all variables here are independent from each other. Comment on the usefulness in developing a marketing plan. The R2 coefficient is not quite linear, the highest is 0.81, therefore Papodopolous should probably not take this that there is a linear relationship between the group size and amount spent there could be other factors at play.

However, he could take the low standard error in the German and French groups to take it that spending behavior is not widely spread within these groups with respect to the mean spending. Task(g) – Estimate for the spending of a family of 2 adult and 4 children. British German French Italian Estimate 618.49 621.01 567.64 604.62 Comment on the statistical significance. When we assume that a group is comprised of 2 adults and 4 children, we can estimate their spending using the assumption of a straight line equation y=mx + c, where m is the regression slope and c is the intercept.

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