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Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

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12 questions

SA-9709-P6-HT-0051 markL1 FoundationCalculatorErrors
A Type I error is
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-HT-0111 markL1 FoundationCalculatorErrors
A Type II error is
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-HT3-0031 markL1 FoundationCalculatorErrors for a mean
A test for a population mean uses the normal distribution at the 5%5\% significance level. State the probability of a Type I error.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-HT3-0061 markL1 FoundationCalculatorErrors
The significance level of a test is reduced from 5%5\% to 1%1\%. What happens to the probabilities of Type I and Type II errors?
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-HT-Q031 markL1 FoundationCalculatorErrors
If a test's probability is 0.070.07 and the significance level is 5%5\%, you should
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-HT3-0012 marksL2 StandardCalculatorErrors
H0:p=0.4H_0:p=0.4, H1:p>0.4H_1:p>0.4, with n=10n=10. H0H_0 is rejected if X≥8X\ge8. Find the probability of a Type I error, correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-HT3-0023 marksL2 StandardCalculatorErrors
For the test in the previous question (n=10n=10, reject H0:p=0.4H_0:p=0.4 if X≥8X\ge8), the true value of pp is 0.70.7. Find the probability of a Type II error, correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-HT3-0052 marksL2 StandardCalculatorErrors
H0:λ=3H_0:\lambda=3, H1:λ>3H_1:\lambda>3, where X∼Po(λ)X\sim\text{Po}(\lambda). H0H_0 is rejected if X≥7X\ge7. Find the probability of a Type I error, correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-HT-0063 marksL3 ExamCalculatorErrors
H0:p=0.25H_0:p=0.25, H1:p<0.25H_1:p<0.25, with n=15n=15. H0H_0 is rejected if X≤1X\le1. Find the probability of a Type I error, correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-HT-0073 marksL3 ExamCalculatorErrors
For the test in the previous question, the true value of pp is 0.10.1. Find the probability of a Type II error, correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-HT3-0073 marksL3 ExamCalculatorErrors
For the test with H0:λ=3H_0:\lambda=3 rejected when X≥7X\ge7, the true value of λ\lambda is 66. Find the probability of a Type II error, correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-HT3-0045 marksL4 ChallengingCalculatorErrors for a mean
A population has standard deviation 66. A test of H0:μ=50H_0:\mu=50 against H1:μ>50H_1:\mu>50 uses a sample of 99 at the 5%5\% level. Find the critical value of xˉ\bar x, and the probability of a Type II error when μ=55\mu=55, each correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme