Q377 · Practice questionTechnology-activeComplex familiar5 marks
QUESTION 377 (5 marks)
Two independent random samples from the same population have no respondents in common. In sample A, of respondents support a proposal. In sample B, of support it. Use .
a)[3 marks]
Use both samples to construct a 95% approximate confidence interval, rounding endpoints to three decimal places.
b)[2 marks]
Evaluate the claim that pooling these results gives a more precise estimate than sample A alone.
WORKED SOLUTION
5 marksPractice marking scheme
ANSWER
a) Pooled interval . b) Sample A alone gives ; pooling gives a narrower interval in this case.
Worked solution
a) The pooled proportion is . The margin is .
b) For A, and the margin is . The pooled width is about , compared with for A. This supports greater precision for these data; the centre also changes.
Exact answers unless rounding is specified; equivalent forms accepted. Retain unrounded intermediate values.
Pools successes and sample sizes correctly.
Calculates the pooled standard error and margin.
Obtains the pooled interval.
Obtains the interval for A alone.
Compares widths and evaluates the precision claim.
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