A survey of a random sample of 1000 likely voters in the US found that 42% said

Question

A survey of a random sample of 1000 likely voters in the US found that 42% said that if the election were held today, they’d vote for Obama and 58% said they’d vote for Romney.

What’s the mean % of people saying they’d vote for Obama?

How many people out of the 1000 said they’d vote for Obama?

How many people out of the 1000 said they’d vote for Romney?

Calculate the standard error of the population proportion (mean) of people who’d vote for Obama (rounded to 2 decimal places – so, if your answer was .039, you’d round it to .04 – by the way, the answer won’t be .039).

Based on your calculations, you can be 95% confident that the mean percentage of people in the population who’d vote for Obama if the election were held today is between what two percentages?

Based on your calculations, you can be 95% confident that the mean percentage of people in the population who’d vote for Romney if the election were held today is between what two percentages?

Based on your calculations, you can be 99% confident that the mean percentage of people in the population who’d vote for Obama if the election were held today is between what two percentages?

Based on your calculations, you can be 99% confident that the mean percentage of people in the population who’d vote for Romney if the election were held today is between what two percentages?

Explanation / Answer

1) p = 0.42 , n =1000

mean for obama = n p = 1000 * 0.42 = 420

2)
42% people vote for obama

3)

58% people vote for romney

4)
Standard error = sqrt(p * (1 - p) / n)
= sqrt(0.42 * 0.58/1000)
= 0.02

5) For obama
z value at 95% = 1.96

CI = p +/- z * sqrt(p * (1 - p) / n)
= 0.42 +/- 1.96 * sqrt(0.42 * 0.58/1000)
= (0.3894 , 0.4506)
= ( 38.94% , 45.06%)

6) For Romney
p =0.58
CI = p +/- z * sqrt(p * (1 - p) / n)
= 0.58 +/- 1.96 * sqrt(0.58 * 0.42/1000)
= (0.5494 , 0.6106)
= ( 54.94% , 61.06%)

7)
For obama
z value at 99% = 2.576

CI = p +/- z * sqrt(p * (1 - p) / n)
= 0.42 +/- 2.576 * sqrt(0.42 * 0.58/1000)
= (0.3798 , 0.4602)
= ( 37.98% , 46.02%)

8) For Romney
p =0.58
CI = p +/- z * sqrt(p * (1 - p) / n)
= 0.58 +/- 2.576 * sqrt(0.58 * 0.42/1000)
= (0.5398 , 0.6202)
= ( 53.98% , 62.02%)

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