BUS105 Use of Descriptive Sample Statistics to Investigate Variable: Computing Assignment Answer

Title: BUS105 Computing Assignment

Semester 1, 2020 

Question 1

a) Just using the information for Country 1

i) Paste in descriptive sample statistics that let you investigate the relationship between the variables “Gender?” and “Would you buy?” using the sample 

ii) Use the output in part (i) to describe the relationship between the two variables, your discussion must use one of the following sample statistics.

The two variables are ‘Gender’ and ‘Would you buy’ and both are categorical in nature. The above descriptive sample table presents absolute numbers and percentage-wise break-up between the two variables. Hence, 11 or 23.91% of the female population is not willing to buy while 35 or 76.09% of the female population is willing to buy. Similarly, 16 or 29.63% of the male population is not willing to buy while 38 or 70.37% of the male population is willing to buy. 

Hence, it is visible that majority of population, be it male or female is willing to buy. Overall, 27 respondents are not willing to buy while 73 respondents are willing to buy. This will used to find difference between proportions:

Difference between sample proportions  -  

 - = 0.73 – 0.27 = 0.46. 

The two proportions used are those who are willing to buy and those who are not willing to buy. The difference between the two proportions is 0.46 or 46% upswing for those willing to buy.

b) Just using the information for Country 2

i) Paste in descriptive sample statistics that let you investigate the claim there is a relationship between the variables “Gender?” and “Would you buy?”

ii) Use the output in part (i) to describe the relationship between the two variables, your discussion must use one of the following sample statistics (chose one)  

The two variables are ‘Gender’ and ‘Would you buy’ and both are categorical in nature. The above descriptive sample table presents absolute numbers and percentage-wise break-up between the two variables. Hence, 18 or 39.13% of the female population is not willing to buy while 28 or 60.87% of the female population is willing to buy. Similarly, 33 or 61.11% of the male population is not willing to buy while 21 or 38.89% of the male population is willing to buy. 

Hence, it is visible that majority of female population is willing to buy but not majority of male population. Overall, 51 respondents are not willing to buy while 49 respondents are willing to buy. This will used to find difference between proportions:

Difference between sample proportions  -  

 - = 0.51 – 0.49 = 0.02. 

The two proportions used are those who are willing to buy and those who are not willing to buy. The difference between the two proportions is 0.02 or 2% upswing for those willing to buy.

c) Compare the results in parts (a) and (b)  

The upswing for those willing to buy is 46% in case of country 1 and 2% in case of country 2. This indicates much stronger willingness to buy the TV model XYZ in Country 1. This is visible in following stacked bar graphs as well:

Question 2

a) Just using the information for country 1

i) Paste in descriptive sample statistics that let you investigate the relationship between the variables “Would you buy?” and “amount you would spend?” using the sample

ii) Use the output in part (i) to describe the relationship between the two variables, your discussion must use one of the following sample statistics (chose one) 

The two variables are ‘Would you buy’ and ‘Amount you would spend’ where one variable is categorical in nature and the other is quantitative in nature. The above descriptive sample table presents mean, standard deviation and count for the two categories (willing to buy and not willing to buy).

Difference between sample means -

 - = 544.704-709.356 = -164.65

Hence, there is an upward swing of 164.65 for those willing to buy.

b) Just using the information for Country 2

i) Paste in descriptive sample statistics that let you investigate the claim there is a relationship between the variables “would you buy?” and “amount you would spend?”

ii) Use the output in part (i) to describe the relationship between the two variables, your discussion must use one of the following sample statistics 

The two variables are ‘Would you buy’ and ‘Amount you would spend’ where one variable is categorical in nature and the other is quantitative in nature. The above descriptive sample table presents mean, standard deviation and count for the two categories (willing to buy and not willing to buy).

Difference between sample means -

 - = 707.569 - 607.898 = 99.67

Hence, there is an upward swing of 99.67 for those not willing to buy.

c) Compare the results in parts (a) and (b)  

In case of Country 1, the mean amount that people are willing to spend indicates upswing for those willing to buy amounting to 164.65. In case of Country 2, the mean amount that people are willing to spend indicates downswing for those willing to buy amounting to 99.67

Question 3

a) Just using the information for Country 1

i) Paste in descriptive sample statistics and a graph that let you investigate the relationship between the variables “Income?” and “Amount you would spend?” using the sample 

ii) Use the output in part (i) to describe the relationship between the two variables, your discussion must use one of the following sample statistics 

The two variables are ‘Income’ and ‘Amount you would spend’ where both variables are quantitative in nature. The above descriptive sample table presents information for correlation and also coefficients for regression equation where sample slope is coefficient for x variable and sample intercept is the intercept value. The r is 0.95 which indicates high degree of positive correlationship between the two variables. As one variable increases, the other also increases and vice versa.

b) Just using the information for Country 2

i) Paste in descriptive sample statistics and a graph that let you investigate the claim there is a relationship between the variables “Income?” and “Amount you would spend?” using the sample

ii) Use the output in part (i) to describe the relationship between the two variables, your discussion must use one of the following sample statistics 

The two variables are ‘Income’ and ‘Amount you would spend’ where both variables are quantitative in nature. The above descriptive sample table presents information for correlation and also coefficients for regression equation where sample slope is coefficient for x variable and sample intercept is the intercept value. The r is 0.985 which indicates very high degree of positive correlationship between the two variables. As one variable increases, the other also increases and vice versa.

c) Compare the results in parts (a) and (b) 

The value of r is positive for both countries indicate that the two variables, ‘income’ and ‘amount they would spend’ are positively correlated. As value of one variable increases, the value of other also increases and vice versa. This is seen in following scatterplots also where the observations are highly concentrated in upward direction.

Question 4

1. Considering all people in the country 1 dataset 
2. What is sample size n:the sample size is n=100 
3. What is the sample proportion of people that would buy the model XYZ TV: the sample proportion of people willing to buy the TV is 0.73  
4. Use the answers in part (i) and (ii) to find the z-score of the sample proportion if you assume the population proportion p=0.5:

X is a binomial variable (people will either buy or not buy TV) with:

Mean = µ = np = 100*0.5 = 50

SD = σ = √np(1-p) = √100*.5*(1-0.5) = √50*.5 = √25 = 5

Sample proportion () = 0.73

z-score = (-p)/ σ  = (0.73-0.50)/5 = 0.046

1. Considering all people in the country 2 dataset 
2. What is sample size n:the sample size is n=100
3. What is the sample proportion of people that would buy the model XYZ TV: the sample proportion of people willing to buy the TV is 0.49  
4. Use the answers to parts (i) and (ii) to find zscore of the sample proportion if you assume the population proportion p=0.5:

X is a binomial variable (people will either buy or not buy TV) with:

Mean = µ = np = 100*0.5 = 50

SD = σ = √np(1-p) = √100*.5*(1-0.5) = √50*.5 = √25 = 5

Sample proportion () = 0.49

z-score = (-p)/ σ  = (0.49-0.50)/5 = -0.002

Question 5

Just using the country 1 data set, more specifically the “variables income” and “would they buy” of the country 1 dataset 

1. Just considering the people that would buy the TV
2. What is sample size, sample mean and sample standard deviation of income 

Using pivot table, the information is as below in highlighted row:

1. find a 95% confidence interval for income 

Confidence interval for income = 

Mean = 69.93, n = 73, SD = 16.18

SD/√n = 16.18/√73 = 1.8937, n-1 = 72, α = 0.05 (2tail)

CI (95%) = 69.93 ± (1.9935)(1.8937) 

= 69.93 ± 3.78

95% CI = 66.15 and 73.71

1. Just considering the people would not buy the TV
2. What is sample size, sample mean and sample standard deviation of income 

Using pivot table, the information is as below in highlighted row:

1. find a 95% confidence interval for income 

Confidence interval for income = 

Mean = 53.33, n = 27, SD = 17.23

SD/√n = 17.23/√27 = 3.3159, n-1 = 26, α = 0.05 (2tail)

CI (95%) = 53.33 ± (2.0555)(3.3159) 

= 53.33 ± 6.82

95% CI = 46.51 and 60.1

Question 6

a) Just using the information for country 1

i) Paste in inferential statistics that measure evidence for the claim there is a relationship between the variables “Gender?” and “Would you buy?” if you consider the whole population 

The p-value is 0.52 which is higher than significance level of 0.05. Hence, the p-value is not significant and we do not have enough statistical evidence to reject the null hypothesis.

ii) Make suitable comments about the output in part (i)

At given level of sig of 0.05, it is concluded that there is no significant difference between the two proportions.

b) Just using the information for country 2

i) Paste in inferential statistics that measure evidence for the claim there is a relationship between the variables “Gender?” and “Would you buy?” if you consider the whole population 

The p-value is 0.03 which is lower than significance level of 0.05. Hence, the p-value is significant and we have enough statistical evidence to reject the null hypothesis.

ii) Make suitable comments about the output in part (i)

At given level of sig of 0.05, it is concluded that there is significant difference between the two proportions.

c) Compare the results in parts (a) and (b)  

In case of country 1, no significant difference between proportions was found while in case of Country 2, significant difference between proportions was found.

Question 7

a) Just using the information for country 1

i) Paste in computer output that measure evidence for the claim there is a relationship between the variables “would you buy?” and “amount you would spend?” if you consider the whole population 

ii) Make suitable comments about the output in part (i)

The p-value is less than 0.05 so there is strong evidence that there is a difference between population means. We reject the null hypothesis. 

We can see that the difference in mean amount of those who are willing to spend and not willing to spend is 164.65 and it is statistically significant as concluded above.

b) Just using the information for country 2

i) Paste in computer output that measures evidence for the claim there is a relationship between the variables “would you buy?” and “amount you would spend?” if you consider the whole population 

ii) Make suitable comments about the output in part (i)

The p-value is less than 0.05 so there is strong evidence that there is a difference between population means. We reject the null hypothesis. 

We can see that the difference in mean amount of those who are willing to spend and not willing to spend is 99.67 and it is statistically significant as concluded above.

c) Compare the results in parts (a) and (b)  

Both the countries indicate statistically significant evidence for difference in mean amount that people are willing to spend (as categorised basis whether they are willing to buy or not). Country 1 indicates average which is higher by 164.65 for those willing to buy as compared to those not willing to buy. Country 2 indicates average which is lower by 99.67 for those willing to buy as compared to those not willing to buy.

Question 8

a) Just using the information for country 1

i) Paste in computer output that measures evidence for the claim there is a relationship between the variables “Income?” and “amount you would spend?” if you consider the whole population 

ii) Make suitable comments about the output in part (i)

The p-value is less than 0.05 so there is strong evidence that there is relationship between the two variables as also indicated by high value of R² of 0.896.

b) Just using the information for country 2

i) Paste in computer output that measures evidence for the claim there is a relationship between the variables “Income?” and “amount you would spend?” if you consider the whole population 

ii) Make suitable comments about the output in part (i)

The p-value is less than 0.05 so there is strong evidence that there is relationship between the two variables as also indicated by high value of R² of 0.969.

c) Compare the results in parts (a) and (b)  

Both countries indicate very strong positive relationship between income and amount they are willing to spend as indicated by high value of R and R² 

Question 9 

OPTION 2

The given report is similar in nature to the one that we are currently doing. The report discusses case of two universities where statistics is being taught using an old method and a new method. 

The variables analysed include attendance of the student, marks of the student and whether they passed or failed the course. Hence, 

1. Attendance which refers to number of classes attended is a quantitativevariable
2. Mark which refers to the students mark is a quantitative variable
3. Did they pass refers to the result and is a categorical variable with output being either pass or fail.
4. Which method refers to the method of teaching and is a categorical variable with output being either old or new.

The report analyses descriptive sample statistics and inferential statistics between various variables.

1. The analysis for two categorical variables, “which method” and “did they pass” uses difference in sample proportions method. P-value method is used under inferential technique.
2. The analysis for two quantitative variables, “attendance” and “marks” uses scatterplot, correlation and regression techniques. P-value method is used under inferential technique.
3. The analysis for one categorical variable, “which method” and one quantitative variable, “attendance” uses difference in sample means method.

The report also compares results for University 1 and University 2 to conclude the inferences based on use of various statistical methods.

Hence, the report is similar in using various techniques and explains how various types of variables can be analysed. The same technique cannot be used for all types of variables and hence, the method varies.