Question

Find an example of a confidence interval for a proportion in the media or scholarly literature (do not use a statistics textbook or website/article that is teaching or demonstrating statistics to find the example) At the very least it must include either the lower and upper bounds or a point estimate with a margin of error Make sure you have a Proportion confidence interval and NOT a CI for the mean, odds ratio, hazard ratio, or relative risk as these will result in having to REDO the assignment (a) Include a digital photo/screenshot of the original appearance of the confidence interval and a link to the website (or citation) where it can be found. (b) Write the confidence interval in the form (lower bound, upper bound). If there are multiple confidence intervals, just pick one. (c) State the population parameter this confidence interval is trying to estimate. (d) State the confidence level and sample size. If no confidence level is given assume it is 95 % . (e) Use the point estimate, confidence level, and sample size to calculate the confidence interval and compare your calculated values with those published in the article. (f) State what the sample and population were for the study. Infer this information if it is not provided (g) Comment on the source for the data, the publisher of the CI, and their purpose for doing so. Put the above in a document and upload your complete file below.

Answer 1

(a) Let's take the pre election poll data of midterm elections of Nevada (USA). Poll data collected by 'The NewYork Times' showed that 'Jacky Rosen' (a congress women) had 45% $\pm$ 4% voters in her favors.

The data is shown below -

The data has been collected from website -

https://www.nytimes.com/interactive/2018/upshot/elections-poll-nvsen-2.html

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(b) As we are interested in confidence interval of proportion of votes in favor of Jacky Rosen, so the required interval is -
(41%, 49%) which is equivalent to (0.41, 0.49).

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(c) This interval is trying to estimate 'The proportion of voters in favor of Jacky Rosen at Nevada'.

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(d) As there is no confidence level given, so we will assume it to be 95%. And note that the sample size = n = 642 because thats the number of people who responded.

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(e) Note that the point estimate is the sample proportion = p = 0.45.

So, the required confidence interval is -

$p \pm1.96 \sqrt{\frac{p(1-p)}{n}} = 0.45 \pm 1.96 \sqrt{\frac{0.45 \times 0.55}{642}}$

So, the estimated confidence interval is : (0.4115, 0.4885)

Rounding it up to 2 decimal places gives (0.41, 0.49) which is exactly what is published in the website.

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(f) The population would correspond to the whole population of Nevada and the sample is the people who responded from different part of the state. Sample is a group of people who responded to the survey call located in different part of state.

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(g) The data is collected via telephonic call which makes it authentic. The publisher is 'The NewYork Times' which is one of the most reputed newspaper in USA and so their data can be trusted. They are trying to predict the winner of midterm elections for Nevada.