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A random sample of 200 businesses showed that 130 of them ban smoking on their premises. Create a 95% confidence interval for the population proportion of all businesses that ban smoking on their premises

User Miro Samek
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1 Answer

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14 votes

Answer:

To create a 95% confidence interval for the population proportion of businesses that ban smoking on their premises, we can use the following formula:

Point estimate ± 1.96 * standard error

Where the point estimate is the sample proportion (130/200 = 0.65), and the standard error is the standard deviation of the sampling distribution of the sample proportion, which can be calculated as:

Standard error = √(sample proportion * (1 - sample proportion) / sample size)

Plugging in the values, we get:

0.65 ± 1.96 * √(0.65 * (1 - 0.65) / 200)

Which simplifies to:

0.65 ± 0.039

Therefore, the 95% confidence interval for the population proportion of businesses that ban smoking on their premises is (0.611, 0.689).

Step-by-step explanation:

SELF EXPLANATORY

User Sergey Avdeev
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