17. (10 points) A small town in southern Louisiana has 422 adult residents. The

Question

17. (10 points) A small town in southern Louisiana has 422 adult residents. The mayor of the town would like to impose an additional propety tax on the residents to raise money to repair the streets. The town council will approve such a tax only if the mayor can show that a majority (more than 50%) of the residents support the tax. The mayor contacted all 422 adult residents and found that 276 of them would be willing to pay the tax. The mayor believes he should conduct a statistical hypothesis test to test the hypotheses H : p = 0.5 s. H : p > 0.5 . Is it appropriate for the mayor to cany out this hypothesis test? Explain.

Explanation / Answer

There is no need to do a hypothesis test here , because we are given that the population size of the town here is 422, and the mayor has done the survey on the whole population itself.

The proportion here is computed as: p = 276 / 422 = 0.6540

Also as the proportion here is way larger than 0.5, therefore in this case there is no need to do the hypothesis test as the point estimate of 0.6502 is sufficient evidence in this case as we did it on the population itself.

( Note that we have not really computed the sample proportion here but we have accurately computed the population proportion itself )

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