Candidates for the Czech presidential elections have to gather 50,000 valid signatures to be eligible. Signature lists submitted by candidates may contain invalid signatures. For a candidate, two random samples of 100 signatures each are drawn and analyzed. Suppose the candidate has submitted 60,000 signatures. In the first sample, the fraction of invalid signature is found to bep1=0.11, and in the second sample the fraction isp2=0.09 (a)If sampling is really random, how likely is it that we would observe such an outcome? (b)Assuming sampling was random, construct a 99% confidence interval of the number of invalid signatures in the 60,000 signatures submitted. (c)The Czech authorities estimate the percentage of invalid signatures by taking the sum ofp1andp2, thus ruling out 12,000 signatures as invalid. What is the likelihood that the candidate, in fact, had more than 50,000 valid votes?
Candidates for the Czech presidential elections have to gather 50,000 valid signatures to be eligible. Signature lists submitted by candidates may contain invalid signatures. For a candidate, two random samples of 100 signatures each are drawn and analyzed. Suppose the candidate has submitted 60,000 signatures. In the first sample, the fraction of invalid signature is found to bep1=0.11, and in the second sample the fraction isp2=0.09
(a)If sampling is really random, how likely is it that we would observe such an outcome?
(b)Assuming sampling was random, construct a 99% confidence interval of the number of invalid signatures in the 60,000 signatures submitted.
(c)The Czech authorities estimate the percentage of invalid signatures by taking the sum ofp1andp2, thus ruling out 12,000 signatures as invalid. What is the likelihood that the candidate, in fact, had more than 50,000 valid votes?
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