142 out of 507 people were right. Calculate a 95% confidence interval for the proportion of the entire population that could be right. I did some of the work and got .72...don't know what to do with this? Please help.

p = 142/ 507 = 0.28

SD = sqrt(p(1-p)/n)

0.28-+ 0.039

(.241, .319)

so I could say that with 95% confidence, between 24.1% and 31.9% of the entire population could be right?

you know I am getting .0199 SD =srt(.28(1-.28)/506 = .0119? Please check for me again?

YES. IF YOUR PROFESSOR SAID THAT YOUR ANSWER SHOULD BE IN PERCENT.

P = 142/507 = 0.28

SD = SQRT( .28*.72/507)

SQRT(0.2016/507) = 0.0199

Z = 1.96

0.28-+1.96*0.0199

0.28-+ 0.039
( 0.241, 0.319)

I get it now...I was missing a step too! Thanks Much!

To calculate the 95% confidence interval for the proportion of the entire population that could be right, you can follow these steps:

Step 1: Calculate the sample proportion. Divide the number of people who were right (142) by the total sample size (507) to get the sample proportion, which is approximately 0.280.

Step 2: Determine the margin of error. The margin of error represents the range within which the true population proportion is likely to fall. It is calculated using the formula:

Margin of Error = critical value * standard error

Step 3: Calculate the critical value. The critical value corresponds to the desired level of confidence. For a 95% confidence interval, the critical value can be obtained from a standard normal distribution table or a statistical calculator. The critical value for a 95% confidence level is approximately 1.96.

Step 4: Calculate the standard error. The standard error measures the variability of the sample proportion and is calculated using the formula:

Standard Error = sqrt((sample proportion * (1 - sample proportion)) / sample size)

In this case, the sample proportion is 0.280 and the sample size is 507, so the standard error is approximately 0.022.

Step 5: Calculate the margin of error. Multiply the critical value (1.96) by the standard error (0.022) to get the margin of error, which is approximately 0.043.

Step 6: Calculate the lower and upper bounds for the confidence interval. Subtract the margin of error (0.043) from the sample proportion (0.280) to get the lower bound, and add the margin of error to the sample proportion to get the upper bound.

Lower bound = sample proportion - margin of error
Lower bound = 0.280 - 0.043
Lower bound ≈ 0.237

Upper bound = sample proportion + margin of error
Upper bound = 0.280 + 0.043
Upper bound ≈ 0.323

Step 7: Interpret the confidence interval. The 95% confidence interval for the proportion of the entire population that could be right is approximately 0.237 to 0.323. This means that we can be 95% confident that the true proportion of the entire population that could be right falls within this range.

Therefore, in your case, the 95% confidence interval for the proportion of the entire population that could be right is approximately 0.237 to 0.323.