We are interested in the number of apps students use on their smartphones per month. Assume that the number of apps used per month by smartphone owners is normally distributed but that the population standard deviation is unknown. The mean of the sample means is calculated to be 19 apps per month. What is the probability that sample mean is between 18.5 and 19.5 if the sample standard deviation (of a sample of size 25) is 4?

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 Ons stel belang in die aantal toepassings wat studente per maand op hul slimfone gebruik. Aanvaar dat die aantal toepassings wat per maand deur slimfooneienaars gebruik word, normal verdeel is, maar dat die populasie standaardafwyking onbekend is. Die gemiddelde van die steekproef gemiddeldes word bereken as 19 toepassings per maand. Wat is die waarskynlikheid dat die steekproef gemiddeld tussen 18.5 en 19.5 is as die steekproef standaardafwyking (van 'n steekproef van grootte 25) 4 is?

A magazine reported that at the top 50 business schools in a region, students studied an average of 17.6 hours. We are interested in finding evidence that the average amount of hours is different from 17.6 hours. Which of the following is an example of a type II error?

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n Tydskrif het beweer dat by die top 50 sake skole in ‘n streek, die studente ‘n gemiddeld van 17.6 ure studeer. Ons stel belang om bewyse te vind dat die gemiddelde hoeveelheid ure verskil van 17.6 ure. Watter van die volgende is ‘n voorbeeld van ‘n tipe II fout?

A business has  employees. You want to estimate the proportion who use the vending machines with a margin of error  with 99% confidence. From a pilot sample a sample proportion of  has been calculated. Considering the sample will be taken without replacement from a finite population. What sample size is required? 

You wish to compute a 95% confidence interval of the population proportion. No prior estimate of the population proportion is available. If you are willing to accept an estimation error of ±0.06, the minimum required sample size is / U wil die 95% vertrouensinterval vir die populasieproporsie bereken. Geen vorige beraming vir die populasieproporsie is beskikbaar nie. Indien u bereid is om ’n beramingsfout van ±0.06 te aanvaar, is die minimum steekproefgrootte wat vereis word

Die steekproefgrootte nodig om die populasieproporsie binne 3% te beraam met 90% vertroue indien ons aanvaar dat die steekproefproporsie 0.28 is, is / The sample size necessary to estimate a population proportion to within 3% with 90% confidence assuming a sample proportion of 0.28 is

Indien [18; 30] die 95% vertrouensinterval vir μ is, word dit as volg geïnterpreteer: / If [18; 30] is the 95% confidence interval for μ, it is interpreted as follows:

Volgens ʼn verslag in Business Week in 2006, toon data dat die meerderheid van maatskappye wat winste verklaar het, vooruitskattings oortref het. ʼn Steekproef van 162 maatskappye toon dat 104 vooruitskattings oortref het, 29 het met vooruitskattings ooreengestem en 29 het swakker gevaar as verwag / According to a Business Week report in 2006, data showed that the majority of companies reporting profits had beaten estimates. A sample of 162 companies showed 104 beat estimates, 29 matched estimates, and 29 fell short.

Bereken die 99% vertrouensinterval vir die populasieproporsie maatskappye wat vooruitskattings oortref het. / Calculate the 99% confidence interval for the population proportion of companies who beat estimates.

ʼn Biostatistikus wil die gemiddelde gewigsverlies van mense op ʼn nuwe dieëtplan beraam. Uit ondervinding weet hy dat die populasie gewigsverlies ʼn standaardafwyking van 5 kilogram het. Hoe groot steekproef moet hy neem om die gemiddelde gewigsverlies binne ʼn interval van 2 kilogram te beraam met 90% vertoue? / A biostatistician wants to estimate the average weight loss of people who are on a new diet plan. He knows from past experience that the standard deviation of the population of weight losses is 5 kilograms. How large a sample should he take to estimate the mean weight loss to within an interval of 2 kilograms, with 90% confidence?

Indien die verskil tussen die beramer en die parameter afneem namate die steekproefgrootte toeneem, sê ons die onsydige beramer is / If the difference between the estimator and the parameter decreases as the sample size increases, we call the unbiased estimator

ʼn Steekproef van 80 brandbestryders lewer ʼn gemiddelde ouderdom van 45.2 jaar. Aanvaar die populasiestandaardafwyking is 7.8 jaar. Die 95% vertrouensinterval vir die gemiddelde ouderdom van brandbestryders is / A sample of 80 fire fighters yields an average age of 45.2 years. Assume the population standard deviation is 7.8 years. The 95% confidence interval for the average age of fire fighters is