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).