Simple statistics question.

Simple statistics question?

• To get a voter initiative on a state ballot, petitions that obtain 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 check them against local voter lists. Only 1772 of them turn out to be valid. I am suppose to... Find the correct statistical procedure to use Define the parameter(s) to be used in words If the problem is a hypothesis test, write down the Ho and Ha Would appreciate the help, thank you

• Answer:

  1) You will use a proportional z test. 2) The required proportion to get the petition approved is 250000 / 304266 = 0.82165 The sample proportion of valid signatures is 1772 / 2000 = 0.886 Let p the sample proportion of valid signatures. Let π the true proportion of valid signatures. Ho: π = 0.82165 Ha: π < 0.82165 Test Statistic: z = (p - πHo) / √[πHo(1 - πHo) / n] z = (0.886 - 0.82165) / √[0.82165(1 - 0.82165) / 2000] z = 7.5176 P-value = P(z < 7.5176) ≈ 1 Fail to reject Ho at any reasonable significance level.