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2.5 Statistical Hypothesis Testing

2.5 Statistical Hypothesis Testing

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Question 84

A factory manufactures steel rods with length L L\,L cm, where L∼N(μ,σ2)L \sim \mathrm{N}(\mu, \sigma^2)L∼N(μ,σ2). From a random sample of rods, an 80% confidence interval for μ \mu\,μ is calculated as (74.36,75.64)(74.36, 75.64)(74.36,75.64).

a.

Find a 95% confidence interval for μ\muμ.

[5]
b.

Using the formula for the volume of a rod V=10LV = 10LV=10L, find a 95% confidence interval for the mean volume of these rods.

[2]
c.

If four independent random samples are taken and a 95% confidence interval for μ \mu\,μ is calculated for each, find the probability that at least three of these intervals will contain the true value of μ\muμ.

[4]
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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