Petitions To get a voter initiative on a state ballot, peti-tions that contain at least 250,000 valid voter signatures must be filed with the Elections Commission. The boardthen has 60 days to certify the petitions. A group wantingto create a statewide system of universal health insurancehas just filed petitions with a total of 304,266 signatures.As a first step in the process, the Board selects an SRS of2000 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 submittedmust be valid in order to have the initiative certifiedby the Elections Commission?c) What will happen if the Elections Commissioncommits a Type I error?d) What will happen if the Elections Commissioncommits a Type II error?e) Does the sample provide evidence in support ofcertification? Explain.f) What could the Elections Commission do to increasethe power of the test?

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Petitions To get a voter initiative on a state ballot, peti-
tions 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?
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