To get a voter initiative on a state ballot, petitions that contain at least 250,000 valid voter signatures must be filed with the Elections Commission. The board then has 60 days to certify the petitions. A group wanting to create a statewide system of universal health insurance has just filed petitions with a total of 304,266 signatures. As a first step in the process, the Board selects an SRS of 2000 signatures and checks them against local voter lists. Only 1772 of them turn out to be valid.

a) What percent of the sample signatures were valid?

b) What percent of the petition signatures submitted must be valid in order to have the initiative certified by the Elections Commission?

c) What will happen if the Elections Commission commits a Type I error?

d) What will happen if the Elections Commission commits a Type II error?

e) Does the sample provide evidence in support of certification? Explain.

f) What could the Elections Commission do to increase the power of the test?