Question

in a certain state, a survey of 600 workers showed that 35elonged to a union. find the 95onfidence interval of true proportion of workers who belong to a union.

Answer 1

To find the 95% confidence interval for the true proportion of workers who belong to a union in a certain state, use the formula CI = p_hat ± z * sqrt((p_hat * (1 - p_hat)) / n), where CI is the confidence interval, p_hat is the sample proportion, z is the z-score, and n is the sample size.

Step-by-step explanation:

To find the 95% confidence interval for the true proportion of workers who belong to a union in a certain state, we can use the formula:

CI = p_hat ± z * sqrt((p_hat * (1 - p_hat)) / n)

Where CI is the confidence interval, p_hat is the sample proportion (35/600), z is the z-score corresponding to the desired confidence level (95% corresponds to a z-score of approximately 1.96), and n is the sample size (600)

Plugging in the values, we get

CI = 0.0583 ± 1.96 * sqrt((0.0583 * (1 - 0.0583)) / 600)

Simplifying, we find the confidence interval is approximately (0.0304, 0.0863). Therefore, we can be 95% confident that the true proportion of workers who belong to a union in the state is between 3.04% and 8.63%.