10 questions🇬🇧English
🎯 Binomial Hypothesis Testing – A-level
Maths · A-level — practise hypotheses, critical regions, significance levels and writing conclusions in context.
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Questions
A coin is tested to see whether it is biased towards heads. What is the null hypothesis?
H₀: p ≠ 0.5
H₀: p = 0.5
H₀: p > 0.5
H₀: p < 0.5
20s
Jo claims a die lands on six less often than it should. Which alternative hypothesis should she use?
H₁: p = 1/6
H₁: p ≠ 1/6
H₁: p > 1/6
H₁: p < 1/6
20s
Which of these is a required condition for modelling X with a binomial distribution B(n, p)?
The mean must equal the variance
The trials are independent of each other
The number of trials must exceed 30
The probability p must equal 0.5
20s
A spinner lands on red with probability 0.2. Asif suspects this probability has changed. Which type of test should he use?
Two-tailed, as no direction is specified
One-tailed, as only one value of p is tested
Two-tailed, as each spin has two outcomes
One-tailed, as 0.2 is less than 0.5
30s
A two-tailed binomial test is carried out at the 5% significance level. What is the maximum probability allowed in each tail?
1%
5%
10%
2.5%
20s
What does it mean to say that a hypothesis test is carried out at the 5% significance level?
P(rejecting H₀ when H₀ is true) is at most 5%
The probability that H₁ is true is 95%
Exactly 5% of the trials will be successes
The probability that H₀ is true is 5%
30s
H₀: p = 0.3, H₁: p > 0.3 for pupils walking to school. In a sample, 9 walk and P(X ≥ 9) = 0.1133. Conclusion at 5%?
Enough evidence that under 30% walk to school
Enough evidence that over 30% walk to school
Not enough evidence that over 30% walk to school
This proves exactly 30% walk to school
30s
X ~ B(10, 0.5), H₁: p > 0.5, 5% level. P(X ≤ 7) = 0.9453 and P(X ≤ 8) = 0.9893. What is the critical region?
X ≥ 8
X ≥ 10
X ≥ 7
X ≥ 9
30s
X ~ B(20, 0.25), H₁: p < 0.25, 10% level. P(X ≤ 2) = 0.0913 and P(X ≤ 3) = 0.2252. What is the actual significance level?
0.1
0.0669
0.0913
0.2252
60s
H₀: p = 0.5, H₁: p ≠ 0.5, X ~ B(20, 0.5), 5% level. P(X ≤ 5) = 0.0207 and P(X ≤ 6) = 0.0577. What is the critical region?
X ≤ 4 or X ≥ 16
X ≤ 5 or X ≥ 15
X ≤ 5 or X ≥ 16
X ≤ 6 or X ≥ 14
60s