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## 1. The town of Hayward (California) has about 50,000 registered voters. A political scientist takes a simple random sample of 500 of these v

Question

1. The town of Hayward (California) has about 50,000 registered voters. A political scientist takes a simple random sample of 500 of these voters. In the sample, the breakdown by party affiliation is Republican 115 Democrat 331 Independent 54

The range from _______ to __________ is a 95% confidence interval for the percentage of independents among _________________________. Fill in the first two blanks with numbers. Fill in the last blank with one of the following two options: “All the 50,000 voters in the population”, “500 voters in the sample”.

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2021-09-14T21:17:12+00:00
2021-09-14T21:17:12+00:00 1 Answer
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## Answers ( )

Answer:The range from

8.08%to13.52%is a 95% confidence interval for the percentage of independents amongthe 50000 registered votersof the town of HaywardStep-by-step explanation:A

confidence intervalis “a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval”.The

margin of erroris the range of values below and above the sample statistic in a confidence interval.Normal distribution, is a “probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean”.represent the real population proportion of interest

represent the estimated proportion for the sample of independents

n=500 is the sample size required (variable of interest)

represent the critical value for the margin of error

The population proportion have the following distribution

The confidence interval would be given by this formula

For the 95% confidence interval the value of and , with that value we can find the quantile required for the interval in the normal standard distribution.

And replacing into the confidence interval formula we got:

And the 95% confidence interval would be given (0.0808;0.1352).

The range from

8.08%to13.52%is a 95% confidence interval for the percentage of independents amongthe 50000 registered votersof the town of Hayward