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2.5 Statistical Hypothesis Testing

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Question 81

Andy gets a tennis serve in court independently with probability 0.6.

a.

For 20 serves, find the probabilities of exactly 15 in court and of more than 15 in court. Andy's coach then thinks the probability has changed after 35 of 50 serves are in court. For part (b), use H0:p=0.6H_0:p=0.6H0​:p=0.6, H1:p≠0.6 H_1:p\ne0.6\,H1​:p=0.6 and Y∼B(50,0.6)Y\sim B(50,0.6)Y∼B(50,0.6) under H0H_0H0​.

[3]
b(i).

Explain why the upper-tail probability should be compared with 0.05 for a 10% two-tailed test.

[1]
b(ii).

Calculate P(Y≥35)P(Y\geq35)P(Y≥35).

[2]
b(iii).

State the conclusion.

[1]
Markscheme

2.5 Statistical Hypothesis Testing Questions

  1. A Level
  2. /Maths
  3. /2.5 Statistical Hypothesis Testing

355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.

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