Question

Forty-five percent of employers said that their employees are fairly paid, while only 26% of the employees agreed. if 50 employers and 200 employees were surveyed, find the 99% confidence level of the proportions for each group. round your answers to at least three decimal places.

Answer 1

For the employees, the confidence interval is approximately 0.214 to 0.306.

Step-by-step explanation:

To calculate the confidence interval for the proportions, we can use the formula:

CI = p ± Z * √((p * (1 - p)) / n)

Where:

• CI is the confidence interval
• p is the sample proportion
• Z is the z-score corresponding to the desired confidence level (2.575 for 99% confidence)
• n is the sample size

For the employers, the sample proportion is 0.45 and the sample size is 50. Substituting these values into the formula, we get:

CI = 0.45 ± (2.575) * √((0.45 * (1 - 0.45)) / 50)

Calculating this gives us a confidence interval of approximately 0.324 to 0.576.

Similarly, for the employees, the sample proportion is 0.26 and the sample size is 200. Substituting these values into the formula, we get:

CI = 0.26 ± (2.575) * √((0.26 * (1 - 0.26)) / 200)

Calculating this gives us a confidence interval of approximately 0.214 to 0.306.