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2.5 Statistical Hypothesis Testing

2.5 Statistical Hypothesis Testing

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Question 264

A company states that each pen is defective with probability 0.08.

a.

Find the probability that at least 2 of a sample of 15 pens are defective. An employee then claims that the defect probability exceeds 0.08 after three of a random sample of 20 pens are defective. For part (b), use H0:p=0.08H_0:p=0.08H0​:p=0.08, H1:p>0.08 H_1:p>0.08\,H1​:p>0.08 and X∼B(20,0.08)X\sim B(20,0.08)X∼B(20,0.08) under H0H_0H0​.

[2]
b(i).

Calculate the exact p-value.

[2]
b(ii).

State the decision at the 5% level and give a conclusion in context.

[2]
b(iii).

Describe a Type I error in this context.

[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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