Download or read it online for free here: Read online online html. Quick Notes - Statistics by Walter Antoniotti - 21st Century Learning Products Walter Antoniotti's book is for people with a limited mathematics background who want to learn the material covered in a traditional college statistics course and for people who want to learn statistics to enhance their career. Weatherburn - Cambridge University Press This book provides the mathematical foundations of statistics.
It explains the principles, and proves the formulae to give validity to the methods of the interpretation of statistical data. It is of interest to students of a wide variety of subjects. This book is geared to the high school audience and is specifically tailored to be aligned with the AP Statistics curriculum.
The management are advised to close the Claremont branch since it is unprofitable. The assumption is satisfied. Accept H0. Management conclusion Conclude that flight delay times, on average, do not exceed 10 minutes. ACASA management do not need to conduct an indepth investigation on flight delays. Management conclusion Conclude that the average number of claims processed daily does not exceed Thus the supervisor has no statistical grounds for requesting additional staff.
The histogram is only moderately skewed to the right. Thus reject H0. The machine is not yet due for a full maintenance service. Exercise 9. Therefore, use the pooled-variances t -test to test for differences in means. Therefore, use the unequal-variances t -test to test for differences in means. Recommendation Since there is no difference in mean commuting times, either mode of transport can be prioritised for upgrading or both can be upgraded simultaneously. Management conclusion Conclude that there is no difference in the mean month-end credit card balances between Mastercard holders and Visa Card holders.
Management conclusion Conclude that the mean job satisfaction score for non-attendees is significantly lower than the mean job satisfaction score for job enrichment attendees.
Thus, the statistical evidence supports the view that the job enrichment workshops significantly increased job satisfaction levels of sales consultants. Management conclusion There is no difference in the mean claims settlement time between the two Funds. Thus, the statistical evidence does not support the view that the Green-Aid Medical Fund settles claims sooner, on average, than the Explorer Medical Fund.
Gas ovens are therefore, not faster, on average, than electric ovens. Conclude that the two population variances are equal. Management conclusion Conclude that the mean size of orders received by the Cape Town branch is significantly larger than the mean size of orders received by the Durban branch.
Thus the Cape Town branch is performing better than the Durban branch in terms of average order size. Management conclusion Conclude that there is no significant difference in the mean order sizes between the Cape Town branch and the Durban branch. Thus there is no evidence to believe that the Cape Town branch is performing better than the Durban branch in terms of average order size. The operations manager can be more confident that there is no difference in mean performance between the two branches conclusion based on b.
Now conduct the t-test for equal means, using the pooled-variances t-test approach. Management conclusion Conclude that there is no difference in the mean weekly sales of one-litre cartons of apple juice between the pyramid-shaped and barrel-shaped carton designs.
Thus the marketer can choose either package design to achieve higher weekly sales. Sample data Fruit Puffs Fruity Wheat n x 54 36 pi 0. Management conclusion Conclude that there is no difference in the percentage of consumers who prefer each type of fruit-flavoured wheat cereal.
The marketer can therefore choose to launch either fruit flavour of wheat cereal. Sample data Male Female n x 46 21 pi 0. Reject H0 Management conclusion Conclude that there is a difference in the proportion of males compared to the proportion of females who enjoy listening to jazz.
By inspection , proportionately more males than females enjoy listening to jazz. Hence conclude that there is a difference in the proportion of males compared to the proportion of females who enjoy listening to jazz.
Sample data Status Elite n x 48 55 pi 0. Management conclusion Conclude that proportionately more Elite cheque account clients are overdrawn compared to Status cheque account clients. Hence conclude that proportionately more Elite cheque account clients are overdrawn compared to Status cheque account clients. Use the pooled-variances t -test to test for differences in means. DIST - DIST Conclude that machine 1 produces scrap at a significantly lower average daily rate than machine 2.
Management conclusion Conclude that the KZN plant produces water of a higher quality fewer impurities, on average than the Free State plant. DIST 2. Same conclusion as in a applies.
Management conclusion Conclude that the mean fat content of meat between the Namibian producer and the Little Karoo producer is the same.
Same management conclusion as in a iii above. Thus the two samples are not independent. Management conclusion Conclude that there has been a significant increase in mean sales of ml bottles of disinfectant liquid from before to after the promotional campaign.
Management conclusion Conclude that there has been a significant decrease in the average level of household debt from a year ago.
Same statistical and management conclusions as b above. Stated differently, are the outcomes associated with two categorical variables independent of each other or not? Exercise It appears therefore that a statistical association exists between gender and motivation level.
Therefore conclude that there is a statistical association between the gender of an employee and their level of motivation. The nature of the relationship is described in a above.
Therefore conclude that there is no statistical association between the employment status of a customer and their use of the internet for shopping purposes.
These two events are statistically independent. H1: There is an association between Age of car buyer and Car Size bought. Therefore conclude that there is a statistical association between the age of a car buyer and the size of car bought. Under 30's tend to prefer larger cars; year age car buyers marginally tend towards medium to large cars, while over 45's strongly tend to prefer smaller cars. Recommendation Target larger cars to the younger market and smaller cars to the older market.
Therefore conclude that the proportion of people who read Sports News is the same in each Geographical Region. The evidence is however not strongly convincing. Therefore conclude that gender and preferred gym activity are associated. New conclusion There is no statistical association between gender and gym activity i. Management conclusion By an inspection of the row percentage table in a , it can be concluded that spinning and swimming are the most preferred gym activities of females, while doing the circuit is the least preferred gym activity of females.
H1: The frequency of store visits per week differs significantly from the manager's belief. Therefore conclude that the shopping frequency of customers differs significantly from the manager's belief. These differences are however not strongly significantly different. H1: There is a significant change in the equity portfolio mix between and Therefore conclude that there is no significant change in the equity portfolio mix of the investor between and The equity portfolio profile is essentially the same in as it was in H1: There is a significant change in the payment method for electronic goods.
Therefore conclude that there is a significant shift in payment practices from the past. H1: Limpopo sales pattern does not follow the national sales pattern. Therefore conclude that the Limpopo sales pattern of cereal package sizes differs significantly from the national sales pattern of package sizes sold. By an inspection of the Limpopo sales profile relative to the national pattern, Limpopo tends to sell more large sized packages relative to the national pattern.
The evidence is however not overwhelming i. Therefore conclude that the support for the present compensation plan is different in at least one of the provinces. H0: There is no association between payment plan preference and province. H1: There is an association between payment plan preference and province.
New conclusion There is no statistical association between payment plan preference and province. The sample evidence is not strong enough i. Technical defects however tend to be more prevalent during the night shift.
Thus there does appear to be an association between shift and nature of tyre defects. H1: There is an association between nature of tyre defect and shift. Therefore conclude that the nature of tyre defects produced is related to the shift on which the defects occur. The sample proportions being compared are: Morning Afternoon Night 0.
Based on the row percentages table in a above, it is clear that the morning shift produces a proportionally larger percentage of defective tyres due to mechanical factors than the afternoon or night shifts.
Males, alternatively, are marginally more interested in the Sport and Business sections. These observational conclusions are, however, not overwhelmingly conclusive. H0: There is no association between gender and the newspaper section most preferred. H1 : There is an association between gender and the newspaper section most preferred.
Therefore conclude that gender and the newspaper section most preferred are statistically associated. The sample proportions being compared are: Sport Social Business 0. Based on the row percentages table in a above, it is clear that females tend to read the Social section most, with the Sports section read the least.
H0: There is no change in the size of car loan applications from four years ago. H1: There is a significant shift in the size of car loan applications from four years ago. Therefore conclude that there has been a significant shift in the size of car loan applications from 4 years ago. The shift has been towards larger car loan applications. H0: There is no association between milk type purchased and health-concious status.
H1: There is an association between milk type purchased and health-concious status. Therefore conclude that there is a significant statistical association between the health-concious status of a consumer and their preference for certain type of dairy milk products. The sample proportions being compared are: fat-free low-fat full cream 0. Based on the row percentages table in a above, it is clear that health-concious consumers tend to purchase more fat-free dairy products than full cream products.
It is a measure of the level of influence of the treatment factor on the response measure. Any differences can be attributed to or explained by the influence of the treatment factor on the numeric response measure. Conclusion: All population means are equal. Therefore conclude that there is at least one motor vehicle type with a different average fuel consumption to the rest. By inspection, it would appear that VW has an average fuel consumption that is significantly different higher, and hence least fuel efficient from Peugot and Ford.
Note: The sample evidence must be more convincing i. Assumption 2 A normally distribution population for the response variable. Therefore conclude that there is no difference in the mean volume of sales across the 3 package designs. All are likely to generate the same average sales. Therefore the cereal producer can choose any of the three package designs for their new muesli cereal.
Therefore conclude that there is at least one bank that has a different mean service rating score to the other banks. By inspection, it would appear that Bank X has a significantly higher mean service rating score than the other two banks.
The three banks are perceived similarly by customers in terms of their service levels. Note: The reason for the change in conclusion between a and b is that the statistical evidence is only weak i.
Therefore conclude that there is at least one shelf height that generates a different mean level of sales to the other shelves. By inspection, it would appear that shoulder and waist high shelves generate higher average sales of the drinking chocolate product than bottom or top shelves.
Therefore conclude that there is at least machine that has a different mean processing time. By inspection, machine C has a significantly longer mean processing time than either machines A and B. Machine C must not be considered for purchase. The population mean processing times between the two machines A and B are likely to be identical.
Thus the company can purchase either machine A or machine B. Therefore conclude that there is at least one sector with a different mean earnings yield relative to the other sectors. Therefore conclude that there is at least one advertising strategy that results in a different mean level of deodorant sales relative to the other strategies.
On average, the Sophisticated and Trendy strategies appear to be equally effective the difference in sample means does not appear significant. Recommendation: Either the Trendy or the Sophisticated strategy can be adopted.
Therefore the population mean sales from each of the two strategies is likely to be identical. The two strategies are therefore equally effective and either can be adopted by the company. It appears the least effective.
The remaining two strategies Sophisticated and Trendy are equally effective and therefore either can be adopted by the company to promote its new ladies deodorant. These differences do appear to be significant. Therefore conclude that there is at least one sector with a different mean leverage ratio relative to the other sectors.
By inspection, the banking sector has the lowest mean leverage ratio, while construction and manufacturing appear to have similarly high mean leverage ratios. Recommendation The investor is advised to consider either the banking sector with the lowest mean leverage ratio or the technology sector with a marginally higher mean leverage ratio.
This difference may not be statistically significant. The population mean leverage ratios between the Technology and the the Banking sector are therefore likely to be equal. Their mean leverage ratios are likely to be equal.
Since both sectors offer an investor the same lower risk, either or both can be chosen for investment. Therefore conclude that there is at least one training method with a different mean performance score relative to the other training methods.
By inspection, the lecture and audio-visual are the least effective lower mean scores , while on-the-job and the role-play methods are more effective with higher mean scores. Recommendation The training manager is advised to consider either on-the-job training or use role play methods The difference does not appear to be statistically significant. The population mean performance scores between the two training methods is likely to be the same. Both are likely to produce similar high mean performance scores.
In two-factor ANOVA, two categorical factors are used to explain possible differences between the observed sample means. It is constructed from the sample means of the various combinations of the different factor levels. Alternatively, its p-value 0. If Arts graduates are employed, they must be given intensive marketing training. Hence all switch devices are likely to have the same average dropped call rate. Factor: Interaction effect Since F-stat 4. By contrast, average rubber wastage of radial tyres is lowest on TAM3 3.
Correlation analysis measures the strength of the relationship between the two numeric variables used in the regression equation. There is no statistically significant relationship between x and y. The more the training received, the higher the output. This is a high level of explained variation. Hence training input is very beneficial to worker output and the training programmes should be continued.
As inventory turnover increases, earnings yields also increases. Thus the business analyst's view is supported by the strong sample evidence. Hence inventory turnover has been shown to have a significant direct effect on a company's earnings yield. Yes, the regression equation can by used with confidence to estimate earnings yield based on a company's level of inventory turnover. Conclude that there is a strong positive association between inventory turnover and earnings yield.
Conclude that there is a strong direct association between age of machines and the level of annual maintance costs in Rands. Alternatively, for every year older, the annual maintenance costs increase by R5. The association between aptitude score and performance rating is not statistically significant. Therefore, the call centre manager should have low confidence in this estimated performance rating score. Conclude that the overall model is statistically significant.
For B : Since t-stat For C : Since t-stat 1. For D : Since t-stat 1. Hence, do not reject H0 if Conclude the overall model is statistically significant. Satisfaction : Since t-stat Commitment : Since t-stat Yes, organisational commitment does play a statistically signficant role in explaining employee absenteeism see c , d and e above.
Speed : Since t-stat 3. Viscosity : Since t-stat 1. MB : Since —t-crit Marketing methods B and C can be combined as there is no statistically significant difference between them with regards to their average productivity levels across consultant. MA : Since its p -value 0. MB : Since its p -value 0.
R2 Cape : Since t-stat 1. Example A quantity index measures changes in consumption levels over time, holding prices constant. A price relative is a change in the level of activity of an item in a given period relative to a base period.
This removes the influence of price increases. SmartAccess on the other hand showed an increase in price from to of However, the number of Programmers, on the other hand, reduced by The price of the HQ32 printer cartridge has decreased by 4.
However, the average price of print cartridges decreased by 0. In , prices were 2. Baltic Insurance showed a 6. Hence Federal Insurance showed the bigger claims increase from to Hence Baltic Insurance. The largerst price change increase was sugar with a Quantity c Food items Relatives Milk litres 98 The largest consumption change decrease was sugar with a
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