Question

A poll found that people from the north now have relatively warm feelings toward people from the south. a​ poll, conducted by telephone among a random sample of 981 ​adults, found that 795 of those sampled consider the two regions friends. the margin of error for the poll was plus or minus 2.5 percentage points​ (for a 0.95 confidence​ level). use this information to obtain a 95% confidence interval for the percentage of all northerners who consider the two regions friends.

Answer 1

To find the 95% confidence interval for the proportion of all northerners who consider the two regions friends, calculate the sample proportion (795/981), and add and subtract the given margin of error (2.5 percentage points) after converting it to proportion form (0.025).

Step-by-step explanation:

To calculate the 95% confidence interval for the percentage of northerners who consider the two regions friends, we can apply the formula for a confidence interval for a population proportion, which is p ± Z*(√(p(1-p)/n)), where p is the sample proportion, Z is the Z-score corresponding to the confidence level, and n is the sample size. In this problem, p = 795/981. Since the margin of error is already provided as ± 2.5 percentage points, the confidence interval is simply the sample proportion plus and minus the margin of error.

The calculation is as follows:

• Convert the margin of error to a proportion by dividing by 100: 2.5/100 = 0.025.
• Add and subtract this value from the sample proportion: 795/981 ± 0.025.
• Calculate these two values to get the upper and lower bounds of the confidence interval.

This results in a 95% confidence interval for the proportion of all northerners who consider the two regions friends.