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In a recent survey of 750 people, 600 people claimed to watch football. Construct a 95% confidence interval for the population proportion of people who watch football.

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Answer:

Using a confidence level of 95%, we can find the margin of error using the formula:

Margin of Error = Z * (sqrt(p * q / n))

where:

- Z is the z-score associated with the confidence level. For a 95% confidence level, Z = 1.96

- p is the sample proportion, which is 600/750 = 0.8

- q is 1 - p, which is 1 - 0.8 = 0.2

- n is the sample size, which is 750

Plugging in the values, we get:

Margin of Error = 1.96 * (sqrt(0.8 * 0.2 / 750)) = 0.032

To find the confidence interval, we subtract and add the margin of error to the sample proportion:

Lower bound = 0.8 - 0.032 = 0.768

Upper bound = 0.8 + 0.032 = 0.832

Therefore, the 95% confidence interval for the population proportion of people who watch football is (0.768, 0.832).

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