Legt1710 Essay

Topics: Statistical hypothesis testing, Null hypothesis, Statistical inference Pages: 5 (1151 words) Published: March 24, 2013
Executive Summary

At the request of Crazy John’s M-Tones, Econometric Consulting Services (DECS) has produced a performance report documenting various aspects of Crazy John’s M-tones customer sample population and drawing an inference towards the population by assessing customer base and usage trends.

To achieve the task of producing descriptive statistics and graphically representing the sample data we had attained from Crazy John’s M-Tones, DECS tabulated the data in Excel. Through the calculation of various statistical indicators (e.g mean, mode, and median) and drawing inferences (hypothesis testing) from the five important variables (gender, satisfaction, frequency, and expense) in the survey we have concluded that:

-Crazy John’s M-Tones has a fairly balanced composition gender ratio -Average age is 20, with majority of the sample population falling between the ages 16-20, indicating a young customer base. -For customer usage patterns, the average downloaded song was 12.21. Included in the sample, a large proportion consisted of reoccurring customers, however it is evident there is also a large group of ‘one-off’ customers.

Statistical Analysis

Descriptive Analysis

Figure 1. Histogram displaying the frequency of each gender that purchased at least one ringtone. Upon observation, the sample has a fairly even and balanced gender composition. From the sample of 200 in the survey, 105 (approximately 52%) were female and 95 (approximately 48%) were male. Although female is greater than male, it does not account for a dominance of a gender since there is only a slight difference.

Figure 2. Histogram displaying the frequency of customers belonging to a particular age group that purchased a ringtone.

The age of the customers in the sample survey has a maximum of 68 and minimum of 13. The range being 55 provides little information due to the outlier customer with the age of 68. The mean age is 20.655 is subjected to extreme values, however due to the relatively large sample space, its effect is quite minute. Median age is 20 and along with the mode age of 17 is subjected to less distortion by the outliers indicates that majority of the customer base lies within ages 16-20, in fact 111 (55.5%) lies within that range. The graph is unimodal and is positively skewed, suggesting that as age increases, number of ringtones purchased decreases. By assessing the above data, there is a clear indication that there is a very young customer base for Crazy John’s M-Tones.

Figure 3. Pie Chart displaying the percentage of the satisfaction of customers who purchased a ringtone. For the satisfaction level of customers, exactly half – 50% of all 200 observations are ‘satisfied’ (3); 31.5% are ‘dissatisfied’ (2). And for the extreme responses, 7.5% are ‘very satisfied’ (4) while 13% are ‘very dissatisfied’ (1). Assessing these observations where 57.5% (3) + (4) are satisfied and 42.5% (1) + (2) are dissatisfied it clear that improvement in increase customer satisfaction is required.

Figure 4. Histogram displaying the frequency of each customer’s expense

Expense of customers varies between $3 to $63 dollars. The mean expense of $31.16 and median expense of $33 may suggest large majority of expenditure is within that range. However because the nature of the histogram is bimodal, the mode age is 3 which indicates a large amount of one-off buyers effectively lowers the median and mean. This is further validated by the histogram whereby the largest proportion of expenditure lies between $41 to $50.

Figure 5. Scatter plot displaying the correlation between overall expense and satisfaction

From the above graph there seems to be a strong positive correlation between expenditure and satisfaction. Through further analysis of descriptive statistics, DECS has calculated the correlation between the two variables to be 0.609113 (between the limits of -1 and +1, +1 being a strong linear...
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