In 2003, petitions were submitted to the California Secretary of State calling for the recall of Governor Gray Davis. Each of California’s 58 counties then had to report the number of valid signatures on the petitions from that county so that the State could determine whether there were enough valid signatures to certify the recall and set a date for the recall election. The following paragraph appeared in the San Luis Obispo Tribune (July 23, 2003):

In the campaign to recall Gov. Gray Davis, the secretary of state is reporting 16,000 verified signatures from San Luis Obispo County. In all, the County Clerk’s Office received 18,866 signatures on recall petitions and was instructed by the state to check a random sample of 567. Out of those, 84.48% were good. The verification process includes checking whether the signer is a registered voter and whether the address and signature on the recall petition match the voter registration.

1. Use the data from the random sample of 567 San Luis Obispo County signatures to construct a 95% confidence interval for the proportion of petition signatures that are valid.

2. How do you think that the reported figure of 16,000 verified signature for San Luis Obispo County was obtained?

3. Based on your confidence interval from Step 1, explain why you think that the reported figure of 16,000 verified signatures is or is not reasonable.