N 2004, the General Social Survey (which uses a method similar to simple random sampling) asked, "Do you consider yourself athletic?" For this question, 255 people said that that they did out of 2373 randomly selected people. What is the standard error of the confidence interval?

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InesWalston InesWalston · Answer 1 · 2018-10-29T06:35:03+01:00

Answer-

The standard error of the confidence interval is 0.63%

Solution-

Given,

n = 2373 (sample size)

x = 255 (number of people who bought)

The mean of the sample M will be,

[tex]M=\frac{x}{n} =\frac{255}{2373} =0.1075[/tex]

Then the standard error SE will be,

[tex]SE=\sqrt{\frac{M\times (1-M)}{n}}[/tex]

[tex]SE=\sqrt{\frac{0.1075\times (1-0.1075)}{2373}}=\sqrt{\frac{0.0959}{2373}}=0.0063=0.63\%[/tex]

Therefore, the standard error of the confidence interval is 0.63%

fichoh fichoh · Answer 2 · 2021-10-28T13:08:57+02:00

The standard error of the confidence interval is given by the relation [tex]\sqrt\frac{pq} {n} [/tex] is 0.64%

Given the Parameters :

The value of p = [tex]\frac{x} {n} = \frac{255} {2372} = 0.1075[/tex]

Plugging the values into the equation :

[tex]\sqrt\frac{pq} {n} = \sqrt\frac{(0.1075 \times 0.8925)} {2373} = 0.0063585 [/tex]

Therefore, the standard error of the confidence interval expressed as a percentage is (0.0063585 × 100%) = 0.64%

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