Business Analytics Evaluation - Assignment Example

Business analytics assignment Name: Course: Instructor: Date: PART 1 MEMORANDUM For Attention: Nancy Guan, Senior Editor 13/05/2015 From: Guo Li, Researcher Regarding: Analysis of New Gen Smartphone dataset Dear Nancy, Following your request for the analysis of the New Generation smartphone usage, I have had the opportunity to undertake the study and to do the analysis. Kindly find the answers to your inquiry below. 1. The mean monthly bill for ALL smartphone users at 90% significance monthly bill at 90% significance Mean 65.95333 Standard Error 3.448909 Median 61 Mode 55 Standard Deviation 42.24034 Sample Variance 1784.246 Kurtosis 19.59007 Skewness 3.360097 Range 337 Minimum 13 Maximum 350 Sum 9893 Count 150 Largest(1) 350 Smallest(1) 13 Confidence Level(90.0%) 5.708443 Taking a sample of 150 users, at 90% confidence level, the total amount spent by the users on smartphone is $9893 in one month. The mean monthly bills for smartphone users is $ 65.95333 with a standard deviation of $42.24034 b) the proportion of ALL smartphone users who are on a post-paid plan The total number of prepaid users are 150. Amongst the 150 subscribers, 85 of them are postpaid users while the remaining 65 are prepaid subscribers. This is shown by the graph below: 2. At 5% significance level, smart phone users spend an average of $65.95333 as their monthly bill. This this is different when the study was undertaken at 95% confidence level where the average was $61.50 on their monthly bill. It is worth noting that the standard deviation at 5% confidence level 42.24034 but the range of the monthly bill remains the same irrespective of the significance level. By testing the hypothesis that smartphone users spend more than $61.50 on their monthly bill at 5% significance level against the hypothesis that smartphone users spend less than $61.50 on their monthly bill at 5% significance level; we came to a conclusion that, on average, smartphone users spend more than $61.50 on their monthly bill 3. From the F-test table below, the p-value is given by 1.438871. The significance level is 0.95 Since the P-value (1.438871) is greater than the significance level (0.95), we fail to reject the null hypothesis hence conclude that; Less than 65% of the Smartphone users are on a postpaid plan. Taking a 5% significance level. In this regard, the statement that Less than 65% of the Smartphone users are on a postpaid plan is statistically correct. 4. The average monthly bill for male and female subscribers are $60.71171 and $80.87179 respectively. The difference of the mean is $20.16008. In determining the difference between the mean, a t-test will be carried out assuming unequal variances. According to t-test below; there is a significance difference in the mean monthly bill between ALL male and ALL female smartphone users. Therefore, the difference in the mean monthly bills between male and female subscribers is statistically significant. The sample of 150 subscribers can be used as a generalization for the entire population. From the sample, it is clear that more women use a lot of money on their phones than women. 5. a) At 90% confidence level and given a mean of $2.50, the sample size will be 731025. That is a sample size of 731025 subscribers will give a mean monthly bill of $2.50 with other factors held constant. b) To estimate a proportion of ALL smartphone users who are on a post-paid plan to within 4%, with 90% confidence, then a sample of 94 subscribers must be used. PART B Appendix 1. a) Monthly bill for all smartphone users monthly bill at 90% significance Mean 65.95333 Standard Error 3.448909 Median 61 Mode 55 Standard Deviation 42.24034 Sample Variance 1784.246 Kurtosis 19.59007 Skewness 3.360097 Range 337 Minimum 13 Maximum 350 Sum 9893 Count 150 Largest(1) 350 Smallest(1) 13 Confidence Level(90.0%) 5.708443 Taking a sample of 150 users, at 90% confidence level, the total amount spent by the users on smartphone is $9893 in one month. The mean monthly bills for smartphone users is $ 65.95333 with a standard deviation of $42.24034. It is worth noting that the standard deviation shows how much the value within the data set varies from the mean. That is, through the standard deviation, the researcher will be able to determine how the values in the data are effectively bunched around the mean of the data. The results above shows a high standard deviation indicating a widely spread standard deviation hence less reliable. According to the statistics above, the highest amount that an individual can use on the smartphone is $350 while the minimum amount is $13. This gives a range of $337 per monthly. The values were obtained at 90% confidence level with a sample size of 150 users. However, a sample of 150 is significant enough and can be used to make a general conclusion about the population. This cuts across the groups regardless of the marital status, sex, living status, states, income and other variables. Nevertheless, most users of smartphone use $55 as monthly bill as shown by the mode of the study. The mode is the value that occurs most often in the dataset and in this case it is $55. b) the proportion of ALL smartphone users who are on a post-paid plan The total number of prepaid users are 150. Amongst the 150 subscribers, 85 of them are postpaid users while the remaining 65 are prepaid subscribers. At 90% significance level, the 85 postpaid subscribers use a mean of $63.04706 monthly bill. Most of the 85 subscribers use $55 monthly as represented by the mode of the data below. The highest amount used by a postpaid subscriber is $150 while the minimum amount used is $14, giving a monthly bill range of $136. In total, all the 85 postpaid subscribers use $5359 as the monthly bill. postpaid monthly bill at 90% significance Mean 63.04706 Standard Error 2.878 Median 60 Mode 55 Standard Deviation 26.53385 Sample Variance 704.0454 Kurtosis 0.313967 Skewness 0.213909 Range 136 Minimum 14 Maximum 150 Sum 5359 Count 85 Largest(1) 150 Smallest(1) 14 Confidence Level(90.0%) 4.786681 The proportion of the postpaid subscribers is shown by the graph below 2. average monthly bill at 5% confidence level monthly bill at 5% significance Mean 65.95333 Standard Error 3.448909 Median 61 Mode 55 Standard Deviation 42.24034 Sample Variance 1784.246 Kurtosis 19.59007 Skewness 3.360097 Range 337 Minimum 13 Maximum 350 Sum 9893 Count 150 Largest(1) 350 Smallest(1) 13 Confidence Level(5.0%) 0.216635 At 5% significance level, smart phone users spend an average of $65.95333 as their monthly bill. This this is different when the study was undertaken at 95% confidence level where the average was $61.50 on their monthly bill. It is worth noting that the standard deviation at 5% confidence level 42.24034 but the range of the monthly bill remains the same irrespective of the significance level. To test for the difference in the mean, we use the single factor Anova. Anova: Single Factor SUMMARY Groups Count Sum Average Variance Column 1 150 9893 65.95333 1784.246 Column 2 0 0 #DIV/0! #DIV/0! ANOVA Source of Variation SS df MS F P-value F crit Between Groups 0 1 0 0 1 0.003945 Within Groups 265852.7 148 1796.302 Total 265852.7 149         Ho: smartphone users spend more than $61.50 on their monthly bill at 5% significance level H1: smartphone users spend less than $61.50 on their monthly bill at 5% significance level From the table above, the p-value is given by 1 for single factor ANOVA. The significance level is 0.95. Since the P-value (1) is greater than the significance level (0.95), we cannot reject the null hypothesis hence conclude that; smartphone users spend more than $61.50 on their monthly bill at 5% significance level. This is complemented by the mean monthly bill that stands at $65.95333, irrespective of gender, income, race and many other factors. 3. The total number of prepaid users are 150. Amongst the 150 subscribers, 85 of them are postpaid users while the remaining 65 are prepaid subscribers. In terms of percentage, the total number of post-paid subscribers amounts to 56.6667% while the number of prepaid subscribers constitute 43.3333% of the total subscribers. This is taken at 5% significance level. To test if the statement is true, F-Test Two-Sample for Variances will be used to test the hypothesis that less than 65% of the smartphone users are on a postpaid plan at 5% significance. Hypothesis Ho: Less than 65% of the Smartphone users are on a postpaid plan. Taking a 5% significance level. H1: More than 65% of the Smartphone users are on a postpaid plan. Taking a 5% significance level. F-Test Two-Sample for Variances   monthly bill postpaid monthly bill prepiad Mean 65.95333 69.75384615 Variance 1784.246 3204.000962 Observations 150 65 df 149 64 F 0.556881 P(F Read More