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Sample proportion question

When an election for political office takes place, the television networks cancel regular programming and instead provide election coverage. When the ballots are counted, the results are reported. However, for important offices such as president or senator in large states, the networks actively compete to see which will be the first to predict a winner. This is done through exit polls, wherein a random sample of voters who exit the polling booth is asked for whom they voted. From the data, the sample proportion of voters supporting the candidates is computed. Hypothesis testing is applied to determine whether there is enough evidence to infer that the leading candidate will garner enough votes to win. Suppose that in the exit poll from the state of Florida during the 2000 year elections, the pollsters recorded only the votes of the two candidates who had any chance of winning, Democrat Al Gore and Republican George W. Bush. In a sample of 765 voters, the number of votes cast for Al Gore was 358 and the number of votes cast for George W. Bush was 407. The network predicts the candidate as a winner if he wins more than 50% of the votes. The polls close at 8:00 P.M. Based on the sample results, should the networks announce at 8:01 P.M. that the Republican candidate George W. Bush will win the state? Select a level of significance by analyzing Type I and Type II errors and clearly show your analysis.

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Solution Preview

Hi there,

Here is my explanation:

The null hypothesis: P<=0.50
The alternative hypothesis: P>0.50
This is one tailed z test. At 0.05 significance level (type I error) the critical value ...

Solution Summary

The solution provides detailed explanation as to proportion based t test, type I error and type II error.