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2.5 Statistical Hypothesis Testing

2.5 Statistical Hypothesis Testing

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Question 55

A pharmaceutical company produces tablets. The mass, X X\,X mg, of the tablets follows a normal distribution N(μ,32)N(\mu, 3^2)N(μ,32). To monitor the production process, a random sample of n n\,n tablets is selected and tested at the 5% level of significance using the following hypotheses:

H0:μ=250andH1:μ>250 H_0 : \mu = 250 \quad \text{and} \quad H_1 : \mu > 250 H0​:μ=250andH1​:μ>250
a.

Find, in terms of nnn, the critical region of the test.

[3]
b.

The probability of a Type II error, when the true mean is μ=252\mu = 252μ=252, is less than 0.10.

Find the minimum value of nnn.

[5]
Markscheme

2.5 Statistical Hypothesis Testing Questions

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

316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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