Calculating the Margin of Error for a 99% Confidence Interval Estimate of a Population Proportion with a Sample Size of 6500

Assume that a sample is used to estimate a population proportion P. Find the margin of error E is that corresponds to the given statistics in confidence level. Round the margin of error to four decimal places99% confidence; n=6500, x=1950

To find the margin of error (E), we can use the formula:

E = z * sqrt((p̂ * (1 – p̂)) / n)

Where:
– E is the margin of error
– z is the critical value corresponding to the desired confidence level
– p̂ is the sample proportion
– n is the sample size

In this case, the confidence level is 99%, which means we need to find the critical value z for a 99% confidence interval

To find the margin of error (E), we can use the formula:

E = z * sqrt((p̂ * (1 – p̂)) / n)

Where:
– E is the margin of error
– z is the critical value corresponding to the desired confidence level
– p̂ is the sample proportion
– n is the sample size

In this case, the confidence level is 99%, which means we need to find the critical value z for a 99% confidence interval.

Since the confidence level is 99%, we have to account for 1% on each tail of the distribution, which gives us (100% – 99%)/2 = 0.5% on each side. Looking up the z-value for a 0.5% tail probability (or 0.005) in a standard normal distribution table, we find that z ≈ 2.576.

Now, we can calculate the margin of error:

E = 2.576 * sqrt((p̂ * (1 – p̂)) / n)

We are given that the sample size (n) is 6500 and the sample proportion (p̂) is 1950/6500 = 0.3.

E = 2.576 * sqrt((0.3 * (1 – 0.3)) / 6500)
E = 2.576 * sqrt((0.3 * 0.7) / 6500)
E = 2.576 * sqrt(0.021 / 6500)
E = 2.576 * sqrt(0.00000323)
E ≈ 2.576 * 0.0018
E ≈ 0.0046 (rounded to four decimal places)

Therefore, the margin of error (E) for a 99% confidence interval estimate of a population proportion with a sample size of 6500 and sample proportion of 0.3 is approximately 0.0046.

More Answers: