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Using the dataset given on the last 3 pages of this document

a) Use a pivot table to make a summary that lets you investigate the relationship between the variables “Which region?” and “How much would they pay for version 1?”. Briefly comment on the relationship between the variables.

b) Make a graph that lets you investigate the relationship between the variables “How much they would pay for version 1” and “How much would they pay for version 2”. Briefly comment on the relationship between the variables.

c) Use a pivot table to make a summary that lets you investigate the relationship between the variables “Which version?” and “would you pay more for version 1”. Briefly comment on the relationship between the variables.

d) Find a 95% confidence interval for the proportion of people that would pay more for version 1.

e) Test the claim that people would pay more than \$900 for version 1 on average.

f) Test the claim there is a relationship between the variables “Which region?” and “How much would they pay for version 1?”.

g) Test the claim there is a relationship between the variables “Which region?” and “Would they pay more for version 1?”.

h) Briefly describe some other variables that could be used in a dataset if you wanted to help a business that makes laptops and explain why the variables would be seful.

(i) Briefly describe what is meant by the phrase “lurking variables”.

j) Briefly describe how you would make a report using the previous answers to the previous questions

Amount paid for version 1 in two regions

Relationship between “which region” and “how much you would buy version 1”

 Row Labels Average of how much would they pay for version 1? A 1016.8 B 1054.4 Grand Total 1035.6

The above table shows the average amount of money the regions will buy version 1. The average region B will buy version 1 is \$1054.4 which is higher than region A which will buy version 1 with an average amount of \$1016.8. Both the regions will pay for version 1 an average amount of \$1035.6

 Row Labels Max of how much would they pay for version 1? A 1198 B 1255 Grand Total 1255

The above table shows that region A paid a maximum of \$1198 which is less than maximum of region B which paid a maximum of \$1255. The maximum from both regions is \$1255

 Row Labels Min of how much would they pay for version 1? A 800 B 819 Grand Total 800

The above table shows that region B is willing to pay more minimum amount of \$819 compared to region A who paid minimum amount of \$800. From both the regions, the minimum amount is \$800

 Row Labels StdDev of how much would they pay for version 1? A 128.3347027 B 118.5726334 Grand Total 124.3682216

The above table shows the variations among the amount paid for version 1 between the regions. Region A shows wide variation with a standard variation of 128.33 while the variation of region B is 118.57 and the overall standard deviation is 124.368

From the tables we can see that region B welcomed version 1 compared to region A.

1. Graph

When we plot the line graph of the two variables, we get the above graph. From the graph we can see the people from both the region that is, region A and region B, would pay more for the version 2 more than they would pay for version 1 of the laptops.

When “How much paid for version 1” is regressed against “How much paid for version 2” we find the relationship between them is linear.

1. Which version against version 1
 Row Labels Average of how much would they pay for version 1? N 1023.575758 Y 1041.522388 Grand Total 1035.6

The above table shows the average amount of money those who would pay more for version 1 or not. The average amount those who would pay more for version 1 is 1041.522 while the average amount those who wouldn’t pay more is 1023.58. For both those who would pay more and those who wouldn’t, the average come to 1035.6.

 Row Labels Max of how much would they pay for version 1? N 1253 Y 1255 Grand Total 1255

The above table shows the maximum amount for those who would pay more is 1255 while the maximum for those who wouldn’t pay more is 1253.

 Row Labels Min of how much would they pay for version 1? N 801 Y 800 Grand Total 800

The above table shows the minimum amount for those who would pay more for version 1 is 800 while the minimum for those who wouldn’t pay more for version 1is 801.

 Row Labels StdDev of how much would they pay for version 1? N 140.564716 Y 116.2473015 Grand Total 124.3682216

The above table shows the standard deviation for those who would pay more for version 1 is 116.25 while for those who wouldn’t pay more for version 1 is 140.56.

1. Confident interval of proportion for people who would pay more for version 1(Bia?ek, 2015);  (Wang, Reich & Horton, 2019).

Variation in amount paid for version 1

 Row Labels Count of how much would they pay for version 1? N 33 Y 67 Grand Total 100

Test the claim that people would pay more than \$900 for version 1 on average.

 Row Labels Average of how much would they pay for version 1? N 1023.575758 Y 1041.522388 Grand Total 1035.6
 Row Labels StdDev of how much would they pay for version 1? N 140.564716 Y 116.2473015 Grand Total 124.3682216

From the z tables, z=1.217 is within the acceptance region, we therefore reject the null hypothesis and conclude that people will pay more than average of \$900

1. To get the relationship between “which region” and “How much they would pay for version1” we use the

From excel we rank the variable “how much they would pay for version 1” by;

=RANK(B3,\$B\$3:\$B\$102,1)

We then use the function SUMIF() to get the totals from region A totals from region B

To get the relationship between “which region” and “How much they would pay for version1” we use the Mann-Whitney U test (Zhao & Ding-Geng, 2018);( Corder & Foreman, 2009).

From excel we rank the variable “how much they would pay for version 1” by;

=RANK(B3,\$B\$3:\$B\$102,1)

We then use the function SUMIF() to get the totals from region A totals from region B

Hard disk is memory disk which is capable of storing information in the computer. Different laptops have different sizes. Some have capacity of 1TB, 500GB, 320GB, 160GB etc. These size of the laptops also affects the taste of people towards them. The prices of the laptops are likely to increase with the increase of their hard disk capacity and since people like laptops with higher capacity. they will go for the laptops with higher disk capacity even if they are expensive. When the companies make the laptops with higher capacity, they will be bought even if they are expensive (Bugnion, Nieh and Tsafrir 2017); ( El Zein and Rendell, 2010).

The generation of the laptops can also influence the marketing of the laptops. The generation in a laptop enables it to load faster or slower when connected to the internet. The generation differs in different laptops and it ranges from one to five (Chen, et al., 2017). The higher the generation of a laptop, the faster it will load when connected to the internet. As the generation goes high there is a likelihood that the price will go up. People prefer to buy the laptops with higher generation even if they are expensive. This can also affect the way people view the laptops meaning they will be sold even if they are expensive (Falsafi & Wenisch, 2014).

Core processor is another feature in the laptops which can affect the taste of laptop lovers. Core processor generally affect how the computer carryout the normal computer processing. As the core processor of the laptop increase, the price of the laptops also increases. Laptops with higher processor are expensive than those with low processor. People who need laptops to do a lot of worker will require laptops with high core processor meaning they will go for the high price laptops.

Proportion of people willing to pay more for version 1

Lurking variable is a variable that is not included under explanatory variable or dependent variable but it can bring effect in the interpretation in the relationship between dependent and independent variables. Lurking variables may lead to make a wrong conclusion on the relationship between variables especially it can show that there is a strong relationship between independent variables and dependent variables or it can simply hide the relationship between variables and show that there is no relationship at all between variables.

For example, the relationship between the proportion of people who would pay more for version 1 of the laptop, it clear that high proportion of people will pay more for version 1. There are two variables being compared here, those who will pay more and version 1 of the laptop. The relationship between these two variable can be seen to be very strong, but the data is clearly examined, it id found that the relationship between the two variables cannot be that strong. Therefore, there must be a variable which was not considered during the creation of the model which influence the reason why high proportion prefer laptop of version 1. For example, the reason why people can go for an expensive laptop is due to their speed and storage capacity. Since the researcher did not consider the storage capacity in his research and the storage capacity influenced the laptop preference, storage capacity becomes our lurking variable(García-Belmonte & Ventosa-Santaulària, 2011) (Sabbaghi & Huang, (2018).

From the data there are four variables researcher used; “which region”, “how much would you pay from version 1”, “how much you would pay for version 2” and “would you pay for version 1”. When the relationships between these variables are developed, it is found that the people from region B have higher average Amount of money they would pay for the version 1 of the laptops compared to average amount of money region A would for the same version of the laptop. For the manufacturer, therefore, it is advisable to manufacture to supply version 1 of the laptops to region B than they would supply version 1 to region A. this option has higher return than if they supply more to region A than region B

From the confident interval of the proportion of people who would pay more for version 1, the total number of people who would pay more for version 1 is high compared to the people who won’t pay more for the version 1.  It clearly shows the version 1 of the laptop is preferred by many people and they are willing even to pay more for it. This can be a greater advantage for the manufacturer to make more of version 1. From the graph, in question b, it is also clear that the prices of version 1 of the laptop were higher than the prices of the version 2 of the laptop. It, therefore, means that the version 1 of the laptop will sell even with the high prices. Company XYZ can therefore focus much attention in manufacturing version 1 of the laptops and mainly supply them to region B.

Company XYZ can also consider adding more features in the laptops manufactured. Features like high hard disk capacity, high core Intel processor and the generation of the laptops can attract customers to the laptops.

References

El Zein, A. H. and Rendell, A. P. (2010). Generating optimal CUDA sparse matrix–vector product implementations for evolving GPU hardware. Concurring and Compuation: Practie and Experience, 2(2), 1-7.

Marshall, A., Jorgensbye, H. I, Rovero, F., Platts, P.J., White, P.C. and Lovett, J. C. (2010). The species–area relationship and confounding variables in a threatened monkey community. American Journal of Primatology, 336( 2010), 72-325.

Bia?ek, J. (2015). Construction of confidence intervals for the Laspeyres price index. Journal of Statistical Computation and Simulation, 85(14), 2962-2973.

Bugnion, E., Nieh, J. and Tsafrir, D. (2017). Hardware and Software Support for Virtualization. Morgan & Claypool Publishers.

Chen, Z. C. Chen, W., Liu, X. and Song, C. (2017). Development of an educational interactive hardware-in-the-loop missile guidance system simulator. Computer Applications in Engineering Education, 26(2).

Corder, G. W. & Foreman, D. I. (2009). Nonparametric Statistics for Non-Statisticians (A Step-by-Step Approach). Hoboken: John Wileys & Sons, Inc.

Del Rosario, Z., Lee, M. & Laccarino, G. (2019). Lurking Variable Detection via Dimensional Analysis. Journal on Uncertainty Quantification, 1(1).

Falsafi, B. & Wenisch, T. F. (2014). A Primer on Hardware Prefetching. Synthesis Lectures on Computer Architecture, 9(1), 1-67.

García-Belmonte, L. & Ventosa-Santaulària,D. (2011). Spurious regression and lurking variables. Statistics and Probabilty Letters, 81(12), 45-97.

Sabbaghi, A. & Huang, Q. (2018). Model transfer across additive manufacturing processes via mean effect equivalence of lurking variables. The Annals for Applied Sstatistics, 12(4), 2409-2429.

Wang, X., Reich, N. G. & Horton, N. J. (2019). Enriching Students' Conceptual Understanding of Confidence Intervals: An Interactive Trivia-based Classroom Activity. American Statitician, 73(1), 50-55.

Zhao, Y. & Ding-Geng, C. (2018). New Frontiers of Biostatistics and Bioinformatics. Durham: Springer.

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