Twee ewekansige steekproewe word uit ʼn groot ouditeursfirma geneem. Die een groep is gevra “Hoeveel ure het jy Dinsdagaand geslaap?” Die tweede groep is gevra “Hoeveel ure het jy Saterdagaand geslaap?”. Gebruik ʼn betekenispeil van 5% en toets vir gelyke variansies. Aanvaar dat die populasies normaal verdeel is en onafhanklik is. Die volgende tabel verskaf ʼn opsomming: / Two random samples were taken from a large auditing firm. The one group of auditors were asked “How many hours did you sleep on Tuesday night?” The second group were asked “How many hours did you sleep on Saturday night?”. Use a 5% level of significance and test for equal variances. Assume that the populations are normal and independent. The following table provides a summary:

Die kritieke waarde vir die hipotese toets is / The critical value for the hypothesis test is

Beskou die volgende hipotese toets: / Consider the following hypothesis test:

H₀: µ₁ - µ₂ = 0

H₁: µ₁ - µ₂ > 0

Die volgende resultate is van steekproewe uit twee onafhanklike populasies verkry: / The following results were obtained from samples from two independent populations:

Steekproef 1 / Sample 1:                 n₁ = 35             x̄₁ = 13.6                    s₁ = 5.2

Steekproef 2 / Sample 2:                 n₂ = 40             x̄₂ = 10.1                    s₂ = 8.5

Bereken die standaardfout indien die populasie variansies as gelyk aanvaar kan word. / Calculate the standard error if the population variances can be assumed to be equal.

Beskou die volgende hipotese toets: / Consider the following hypothesis test:

H₀: µ₁ - µ₂ = 0

H₁: µ₁ - µ₂ > 0

Die volgende resultate is van onafhanklike steekproewe uit twee populasies verkry: / The following results were obtained from independent samples from two populations:

Steekproef 1 / Sample 1:                 n₁ = 35            x̄₁ = 14.6                     s₁ = 6.4

Steekproef 2 / Sample 2:                 n₂ = 40            x̄₂ = 10.8                     s₂ = 8.3

Die standaardfout van   indien die populasievariansies as gelyk aanvaar kan word, is / The standard error of   if the population variances can be assumed to be equal, is

ʼn Groot versekeringsmaatskappy het steekproewe geselekteer van enkellopende en getroude manlike polishouers, en die aantal wat in die laaste jaar ʼn versekeringseis ingedien het, is aangeteken in die onderstaande tabel: / A large insurance company selected samples of single and married male policyholders and recorded the number who made an insurance claim over the past year in the table below:

Konstrueer ʼn 95% vertrouensinterval vir die verskil tussen die proporsies vir die twee populasies. / Construct a 95% confidence interval for the difference between the proportions for the two populations.

Beskou die volgende hipotese toets: / Consider the following hypothesis test:

 H₀: µ₁ - µ₂ = 0

H₁: µ₁ - µ₂ > 0

Die volgende resultate is van onafhanklike steekproewe uit twee populasies verkry: / The following results were obtained from independent samples from two populations:

Steekproef 1 / Sample 1:                 n₁ = 35            x̄₁ = 14.6                     s₁ = 6.4

Steekproef 2 / Sample 2:                 n₂ = 40            x̄₂ = 10.8                     s₂ = 8.3

Watter aannames moet gemaak word om die hipotese te kan toets? / Which assumptions need to be made to test the hypothesis?

Om die 95% vertrouensinterval vir die verskil van twee populasie-proporsies te bepaal, oorweeg die tabel met relevante statistieke hieronder en bereken die waarde van die standaardfout. / To determine the 95% confidence interval for the difference between two population proportions, consider the table with relevant statistics below and determine the value of the standard error.

Die uitkoms van 'n eksperiment om vas te stel of die gemiddeles van twee onafhanklike steekproewe verskil, word hieronder weergegee. Bereken die p-waarde.  Aanvaar 'n t-verdeling met 12 vryheidsgrade vir die veranderlike van belang. / The outcome of an experiment to determine if the means of two independent samples differ are provided below. Determine the p-value. Assume a t-distribution with 12 degrees of freedom for the variable of interest.

Beskou die volgende hipotese toets: / Consider the following hypothesis test:

Die volgende informasie word gegee: / The following information is given:

Die waarde van die toetsstatistiek is / The value of the test statistic is

Twee ewekansige steekproewe word uit ʼn groot ouditeursfirma geneem. Die een groep is gevra “Hoeveel ure het jy Dinsdagaand geslaap?” Die tweede groep is gevra “Hoeveel ure het jy Saterdagaand geslaap?”. Gebruik ʼn betekenispeil van 5% en toets vir gelyke variansies. Aanvaar dat die populasies normaal verdeel is en onafhanklik is. Die volgende tabel verskaf ʼn opsomming: / Two random samples were taken from a large auditing firm. The one group of auditors were asked “How many hours did you sleep on Tuesday night?” The second group were asked “How many hours did you sleep on Saturday night?”. Use a 5% level of significance and test for equal variances. Assume that the populations are normal and independent. The following table provides a summary:

Die toetsstatistiek vir die hipotese toets is / The test statistic for the hypothesis test is

Beskou die volgende hipotese toets: / Consider the following hypothesis test:

H₀: µ₁ - µ₂ = 0

H₁: µ₁ - µ₂ > 0

Die volgende resultate is van onafhanklike steekproewe uit twee populasies verkry: / The following results were obtained from independent samples from two populations:

Steekproef 1 / Sample 1:                 n₁ = 35            x̄₁ = 14.6                     s₁ = 6.4

Steekproef 2 / Sample 2:                 n₂ = 40            x̄₂ = 10.8                     s₂ = 8.3

Die kritieke waarde by die 5% betekenispeil indien die populasievariansies as gelyk aanvaar kan word, is / The critical value at the 5% significance level if the population variances can be assumed to be equal, is