The study of statistics 4th edition pdf download

There is also one extremely high unit selling price of Overall, unit selling prices of rosebuds ranged between Finally, the median middle unit selling price achieved was Mini Case Study 3. From the histogram, 21 clients have month-end balances of less than R and 8 are above R Therefore the median month-end balance of R is a more representative indicator of savings balances. Thus they are attracting mainly single females; and married males.

Refer to 1 d Breakdown Table of Average Savings by Gender and Marital Status Single females are saving the most average of R,7 while single males are the worst savers with an average savings balance of only R Also females save more, on average R than males R Single bank clients save more, on average R They should encourage their main client base - married males - to save more.

This means that, on average, members are claiming as much as they contribute. The median claims ratio is a similar value 0. This means that at least half the members are claiming more than they contribute. The distribution see histogram appears to be bi-modal showing a low claims ratio i. Refer to 1 c and d It would appear that married members claim significantly more 1.

Also, the younger members 26 - 35 and older members 46 - 55 claim significantly more 1. The highest claiming segments are the married younger 1. Members from these two segments also have the maximum claims ratio of all members 2. The lowest claiming segment is the middle-aged single members 0. The range of claims ratios is highest amongst married years 0. It is lowest amongst single 36 - 45 year members 0. In conclusion: Younger and Older married members claim more on average - and above their contribution levels in most cases.

The mangement of this medical scheme needs to review member contributions from the married younger and older members. Exercise 4. In c , used the Complementary probability rule In d , used the Addition rule for mutually exclusive events. In c , used the Addition rule for mutually exclusive events. In d , used the Complementary probability rule. In c , the Addition rule for mutually exclusive events.

In d , the Conditional Probability rule. Conclusion: The choice of bonus option and employee work function are associated. Conclusion: There is an association between the Age of an employee and the Department in which they are employed e. Conclusion: Type of usage and choice of brand are associated.

Professionals may prefer Canon while Nikon is favoured by Personal users. Similar for v and viii vi Selecting a committee of 3 persons from 8 candidates, where the first person selected is the chairman, the second is the secretary and the third is a member. Exercise 5. Probability sampling: sample members are chosen using random selection processes so that each target population member stands a chance of being included in the sample.

Every member of the target population has a chance of being included in the sample. This is likely to result in a more representative sample than if a non-probability sampling method was used. Exercise 7. The lower confidence results in a more precise set of interval limits narrower. Since the interval covers 1 litre, it can be concluded that the cartons do contain one litre of milk on average.

Absenteeism per employee ranged between 3 min and 15 days max last year. Thus the company's policy is not being strictly adhered to. Parcel weights ranged between 1. Thus Post-Net is adhering to its policy. Sample size determination Exercise 7.

Exercise 8. Step 2: Determine the region of acceptance of the null hypothesis. Step 3: Compute the sample test statistic. Step 4: Compare the sample test statistic to the region of acceptance. Step 5: Draw the statistical and management conclusions.

Reject H0 Conclude that the population mean value is significantly larger than Reject H0 Conclude that the true population proportion is significantly less than 0. Accept H0 Conclude that the true mean value is equal to 8. Reject H0 Conclude that the true mean value is significantly below Accept H0 Conclude that the true population proportion is equal to 0. Reject H0. Management conclusion Conclude that the population mean value is significantly different from 85 minutes. Visitors to the Knysna shopping mall do not spend 85 minutes on average in the mall.

By inspection of the sample mean, it appears that visitors to the Knysa shopping mall spend significantly less than 85 minutes in the mall. Management conclusion Conclude that the population mean value is at least 30 minutes. The supermarket manager's belief is therefore valid. The sample evidence is not strong enough to refute the belief that customers spend 30 minutes or more, on average, doing their purchases at the supermarket.

Hence conclude that customers are likely to spend at least half-an-hour, on average, in the supermarket doing their grocery shopping.

Management conclusion Conclude that the local importer's claim is valid. Consignments are taking significantly longer than 72 hours to clear customs. Management conclusion Conclude that the Department of Health's concern is justified.

Accept H0 Management conclusion Conclude that Ryeband Bakery is both legally compliant and not wasting ingredients. The average weight of all white loaves produced by Ryeband Bakery is gms. Hence it can be concluded that, on average, the weight of white bread loaves produced by the Ryeband Bakery is gm. Management conclusion Conclude that Ryeband Bakery is not legally compliant.

The average weight of all white bread loaves produced by Ryeband Bakery is significantly below gms. Accept H0 Management conclusion Conclude that mean weekly sales of the new pudding flavour is not less than R The company should therefore not withdraw the product at this stage. Hence it can be concluded that, on average, the weekly sales of the new pudding flavour is not less than R and the product should not be withdrawn. Marathon Products should accept this consignment as it meets quality specs.

Hence it can be concluded that, on average, the tensile strength of the wire in the consignment exceeds 80 kg. Hence accept the consignment. Accept H0 Management conclusion Conclude that the mean fill of one-litre milk containers is not less than 1 litre.

The Consumer Council's claim that containers are being underfilled is not valid. Hence it can be concluded that, on average, the mean fill of milk containers is at least one 1 lite. Thus there is no statistical support for the claim. The company should advertise in this radio station's news timeslots. Accept H0 The company can accept the radio station's claim as valid. The motor vehicle advisor's claim is not valid. Hence the insurance advisor's claim has no statistical validity.

The same management conclusion applies as in a above. The cooperative can justify buying the barley seed from this merchant. The cooperative can accept the seed merchant's claim. Hence do not reject H0. JSE companies are therefore adhering to the rule of thumb. Management conclusion Conclude that the mean transaction value at the Claremont branch is signficantly below R 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. This ICME Topical Survey provides a review of recent research into statistics education, with a focus on empirical research published in established educational journals and on the proceedings of important conferences on statistics education.

It identifies and addresses six key research topics, namely: teachers' knowledge; teachers' role in stat A Concise Guide to Market Research.

This book offers an easily accessible and comprehensive guide to the entire market research process, from asking market research questions to collecting and analyzing data by means of quantitative methods.

It is intended for all readers who wish to know more about the market research process, data management, and the most commonly used methods in m Statistics and Analysis of Scientific Data. The revised 2nd edition of this book provides the reader with a solid foundation in probability theory and statistics as applied to the physical sciences, engineering and related fields. It covers a broad range of numerical and analytical methods that are essential for the correct analysis of scientific data, including probability theory, distribut Lies, Damned Lies, or Statistics.

This is a free textbook for a one-semester, undergraduate statistics course. Social Statistics and Ethnic Diversity.