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2 Statistics

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Question 41

The random variable X X\,X has the distribution X∼B(26,0.40)X \sim B(26, 0.40)X∼B(26,0.40) under the null hypothesis H0H_0H0​: p=0.40p = 0.40p=0.40, and the alternative hypothesis is H1H_1H1​: p≠0.40p \ne 0.40p=0.40, where p p\,p is the population proportion of successes.

A two-tailed test is to be carried out at the 5% significance level, with a probability of at most 0.025 in each tail.

a.

Find the critical region for this test.

[4]
b.

Find the actual significance level of a test based on this critical region.

[1]
c.

Explain why the actual significance level is not equal to 5%.

[1]
Markscheme

2 Statistics Questions

  1. A Level
  2. /Maths
  3. /2 Statistics

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