Question

A statistical survey was conducted in the city of Tirion upon Túna. A sample of 303 residents revealed that 31% were of Vanyar ethnicity. Develop a 99% confidence interval for the population proportion of residents of Vanyar ethnicity (use decimal numbers rounded to the 2nd decimal place). Lower limit: Upper limit:

Answer 1

To develop a 99% confidence interval for the population proportion of residents of Vanyar ethnicity, we can use the formula and substitute the given values. The lower limit is approximately 0.255 and the upper limit is approximately 0.365.

Step-by-step explanation:

To calculate the 99% confidence interval for the population proportion of residents of Vanyar ethnicity, we can use the formula:

Lower limit = p - z * sqrt((p(1-p))/n)

Upper limit = p + z * sqrt((p(1-p))/n)

where p is the sample proportion (0.31), n is the sample size (303), and z is the z-score corresponding to the desired confidence level (approximately 2.58 for a 99% confidence level).

Substituting the values into the formula, we get:

Lower limit = 0.31 - 2.58 * sqrt((0.31(1-0.31))/303) ≈ 0.255

Upper limit = 0.31 + 2.58 * sqrt((0.31(1-0.31))/303) ≈ 0.365

Therefore, the 99% confidence interval for the population proportion of residents of Vanyar ethnicity is approximately 0.255 to 0.365.