# Statistics_Computer assessment Essay Example

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QUESTION 1

1. The survey method is using questionnaire. This is the most appropriate due to large population and various question which will be asked. The questionnaire will consist of both close ended and open ended questionnaire.

2. Simple random sampling is the most appropriate method of sampling technique to be used in this study. This is because it is simple and very much objective in dealing with large population

3. Two main variables is expenditure verses income

4. Reliability of the information which are being provided by the respondent may be in doubt since there is no way the researcher can authenticate the information.

QUESTION TWO

1. The recommended graphical comparison of each weekly take-home pay category should be histograms since they are more clearly giving the level of each frequency at every weekly take-home category. This is shown in the diagram below:- From the graph, it can be seen that group three has the highest frequency of 35 followed by group six with frequency of 30. This is followed closely by group four and two with 26 and 25 respectively group five is the second lowest with 19 frequency and the lowest is group one with 15.

1. Pie chart is the most appropriate in this case as it shows frequency and even the percentage of the proportion. This is shown in the figure below:- From the figure above, group 3 is having the highest propotion of 20% folloed closely by group 2 with 19%, group 4 having 18% while group five having 17%. Group 6 and group 1 are having 13% each and are the lowest.

Question three

1. To determine the number of classes, the following formula is most appropriate

To create grouping for characteristics with equal amplitude you just divide the range (max value -min value) by the amplitude. if you have age between 10 and 90 yrs, if you want classes of 10 yrs amplitude (deciles) then the number of classes is : range/10=(90-10)/10=8 classes.

1. Class width The number of classes is what you want like in this case it is eight. From the data we have

Weekly take home pay

Highest = 1090

Lowest = 105

Class you need = 8

= (1090-105)/8

Highest = 375

Lowest = 44

Class you need = 8

= (373-44)/8

1. Histograms  From the two graphs, take home pay is not normally distributed but it tends to move to left, that is , it is left handed distributed while weekly expenditure is normally distributed to the center.

Question four

1. descriptive statistics

 Take-home pay Weekly food expenditure 501.5866667 197.991266 Standard Error 19.40476241 Standard Error 6.756779581 190.87045 Standard Deviation 237.6588324 Standard Deviation 82.75331139 Sample Variance 56481.72063 Sample Variance 6848.110547 Kurtosis -0.777016935 Kurtosis -0.909166653 Skewness 0.32628762 Skewness 0.088943042 329.1642 373.4779 29698.6899 Largest(1) Largest(1) 373.4779 Smallest(1) Smallest(1) Confidence Level (95.0%) 38.34406623 Confidence Level (95.0%) 13.35148549
1. Correlation coefficient

 Take-home pay Weekly food expenditure Take-home pay Weekly food expenditure 0.994480486

The correlation coefficient is positively correlated and is new 1 or 1 hence there are perfectly positive correlation

Question five

1. From the analysis, food expenditure depends on weekly pay hence food expenditure is the dependent variable while weekly pay is the independent variable in this case

2. Line graph 1. Regression output

 Regression Statistics Multiple R 0.994480486 0.988991437 Adjusted R Square 0.988917054 Standard Error 8.711902022 Observations Significance F Regression 1009135.68 1009135.68 13296.08 8.1E-147 Residual 11232.79105 75.89723684 1020368.471 Coefficients Standard Error Lower 95% Intercept 24.30172358 1.665810737 14.5885262 1.94E-30 21.00988 Take-home pay 0.346280222 0.003003073 115.3086263 8.1E-147 0.340346

From the coefficient table above, the linear equation will be given by

y = 0.3463x + 24.302

The coefficient indicates that it is positively related and a unit increase in weekly pay increases food expenditure by 0.3463 while the intercept where even if there is no monthly income food expenditure will still be 24.302.

1. Correlation coefficient (R2)

From the table, the correlation coefficient is given as 0.988 indicating that 98.8% of the dependent variables is explained by independent variables in the model.