Woolworths Finansiële Dienste wil die proporsie kredietkaarthouers wat ʼn kredietsaldo aan die einde van die maand het, en dus rente koste aangaan, beraam. Aanvaar dat die vereiste beramingsfout ±0.03 is by ʼn 98% vertrouenspeil. Hoe groot steekproef moet geselekteer word indien daar verwag word dat 70% van die kaarthouers ʼn kredietsaldo aan die einde van die maand het? / Woolworths Financial Services wants to estimate the proportion of credit card holders who carry a credit balance at the end of the month and incur an interest charge. Assume that the desired margin of error is ±0.03 at a 98% level of confidence. How large a sample should be selected if it is anticipated that 70% of the card holders carry a credit balance at the end of the month?

Die volgende steekproef is geneem uit ’n normaal populasie. / The following sample was taken from a normal population.

Gegee dat die populasiestandaardafwyking 3.5 is, is die 90% vertrouensinterval vir die populasie gemiddelde / Given that the population standard deviation is 3.5, the 90% confidence interval for the population mean is

’n Vervaardiger van flitsbatterye neem ’n steekproef van agt batterye uit ’n dag se produksie en gebruik hulle aaneenlopend totdat hulle pap is. Aanvaar dat die leeftye normaal verdeel is. Die leeftye van die batterye (in ure) is: / A manufacturer of flashlight batteries takes a sample of eight batteries from a day’s production and uses them continuously until they are flat. Assume that the lifetimes of the batteries are normally distributed. The life times of the batteries (in hours) are:

Konstrueer ʼn 95% vertrouensinterval vir die populasie gemiddelde leeftyd van die batterye. / Construct a 95% confidence interval for the population mean lifetime of batteries.

U is besig om ʼn ondersoek te doen om die gemiddelde inkomste van gesinne in die Noord-Kaap vas te stel. Uit ʼn voorafgaande steekproef weet u dat die standaardafwyking van inkomste van gesinne R500 is. Die borg van die ondersoek wil ʼn vertrouensvlak van 95% gebruik en u beramer moet binne ’n interval van R200 wees. Met hoeveel families moet u onderhoude voer? / You are to conduct a sample survey to determine the mean family income in the Northern Cape. From a previous sample of 10 families, the standard deviation of the income of families is known to be R500. The sponsor of the survey wants you to use the 95% confidence level. The estimate is to be within an interval of R200. How many families should be interviewed?

Die operasionele bestuurder van ʼn suikermeul in Durban wil die gemiddelde grootte van bestellings beraam. Die grootte van ʼn bestelling word gemeet in aantal palette verskeep. ʼn Ewekansige steekproef van 87 bestellings van klante het ʼn steekproefgemiddeld van 131.6 palette. Aanvaar dat die populasiestandaardafwyking 25 palette is en dat die bestellinggroottes normaal verdeel is. Die 90% vertrouensinterval vir die populasie gemiddelde bestellingsgrootte van alle klante is / The operations manager of a sugar mill in Durban wants to estimate the average size of an order received. The size of an order is measured in the number of palettes shipped. A random sample of 87 orders from customers had a sample mean value of 131.6 palettes. Assume that the population standard deviation is 25 palettes and that the order size is normally distributed. The 90% confidence interval for the population mean order size received from all customers is

’n Opname ondersoek die proporsie studente wat ʼn skootrekenaar besit. ’n Ewekansige steekproef van 100 studente word gekies en 56 van hulle het aangedui dat hulle wel ʼn skootrekenaar besit. Die 90% vertrouensinterval vir die proporsie van alle studente wat skootrekenaars besit is / A survey investigates the proportion of students who own a laptop. A random sample of 100 students results in 56 who indicate that they do own a laptop. The 90% confidence interval for the proportion of all students who own laptops is

Youtube.com is een van die webruimtes wat die meeste besoek word op die internet. Volgens navorsing spandeer ’n persoon gemiddeld 46.8 minute op die webruimte met ’n standaardafwyking van 16 minute. Veronderstel die tyd wat ’n persoon op You Tube se webruimte spandeer is normaal verdeel. / Youtube.com is one of the most visited websites on the internet. According to research a visitor spends 46.8 minutes on average on the site with a standard deviation of 16 minutes. Assume that the time an individual spends on You Tube’s website follows a normal distribution.

Indien ons ’n ewekansige steekproef van tien besoeke ondersoek, wat is die waarskynlikheid dat die gemiddelde tyd van hierdie tien besoeke op Youtube.com minder as 50 minute is? / If we select a random sample of ten visits, what is the probability that the average time spent on Youtube.com for these ten visits is less than 50 minutes?

In ’n ewekansige steekproef van 95 studente dui 68 aan dat Statistiek hulle gunsteling vak is. Dit is bekend dat die populasieproporsie 0.70 is. Die standaardfout van die steekproefproporsie is / In a random sample of 95 students, 68 indicate that Statistics is their favourite subject. It is known that the population proportion is 0.70. The standard error of the sample proportion is

Adverteerders betaal soekenjins om advertensies te plaas op hulle webwerwe. Hulle betaal ʼn fooi gebaseer op die aantal potensiële klante wat op hulle advertensies kliek. Ongelukkig het ‘click fraud’ – m.a.w. iemand wat op ʼn advertensie kliek vir die uitsluitlike doel om die advertensieverdienste op te jaag – ʼn probleem geword. Veertig persent van adverteerders beweer dat hulle al die slagoffer van ‘click fraud’ was. Veronderstel ʼn eenvoudige ewekansige steekproef van 380 adverteerders word geneem om die effek van hierdie praktyk te ondersoek. / Advertisers pay search engines to place ads on their websites. They pay a fee based on the number of potential customers who click on their ads. Unfortunately, click fraud – i.e. someone clicking on an ad solely for the purpose of driving up advertising revenue – has become a problem. Forty percent of advertisers claim they have been a victim of click fraud. Suppose a simple random sample of 380 advertisers is taken to study the effect of this practice.

Die waarskynlikheid dat die steekproefproporsie binne ±0.04 van die populasie-proporsie is wat ‘click fraud’ ervaar, is / The probability that a sample proportion will be within ±0.04 of the population proportion experiencing click fraud, is

ʼn Professor in rekeningkunde beweer dat ʼn kwart van voorgraadse ekonomiese- en bestuurswetenskappe studente rekeningkunde as hoofvak sal neem. Indien dit waar is, is die waarskynlikheid dat 336 of meer studente in ʼn ewekansige steekproef van 1200 voorgraadse ekonomiese- en bestuurswetenskap studente rekeningkunde as hoofvak neem / An accounting professor claims that one-quarter of undergraduate economic and management science students will major in accounting. If this is true, the probability that 336 or more students in a random sample of 1200 undergraduate economic and management science students will major in accounting is