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Interval estimates for proportions — Question 317

Original QCE Vault practice · 3 marks

Q317 · Practice questionTechnology-freeSimple familiar3 marks

QUESTION 317 (3 marks)

The diagram shows ten 95%95\% approximate confidence intervals obtained from independent random samples. The dashed line is the true population proportion p=0.4p=0.4.
Ten intervals by sample number: 1 [0.35,0.45]; 2 [0.37,0.47]; 3 [0.32,0.42]; 4 [0.42,0.52]; 5 [0.34,0.44]; 6 [0.38,0.48]; 7 [0.31,0.41]; 8 [0.36,0.46]; 9 [0.28,0.38]; 10 [0.33,0.43]. Dashed vertical true-proportion line p=0.4.
a)
How many of the displayed intervals contain the true proportion?
[1 mark]
b)
Explain why a 95%95\% confidence level does not require exactly 95%95\% of these ten intervals to contain pp.
[2 marks]
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