Suppose 1,600 of 2,000 registered voters sampled said they planned to vote for the Independent candidate for president. Using the 0.95 degree of confidence, what is the interval estimate for the population proportion (to the nearest tenth of a percent)? How to calculate in megastat?
To calculate the interval estimate for the population proportion using Megastat, you can follow these steps:
1. Open the Megastat add-in in Excel.
2. Click on "Descriptive Statistics" and then select "Proportion".
3. A dialog box will appear, where you can enter the data. In this case, enter the number of successes (voters planning to vote for the Independent candidate) as 1600 and the sample size (total registered voters) as 2000.
4. Under the "Options" tab, set the Confidence Level to 0.95.
5. Click "OK" to generate the output.
The output will provide you with the interval estimate for the population proportion. The approximate point estimate will be the proportion of successes in the sample (1600/2000 = 0.8). The confidence interval will be expressed as (lower bound, upper bound), and it will be given as a range of proportions.
Now, let's calculate the interval estimate for the population proportion using the formula:
Step 1: Calculate the point estimate:
Point Estimate (p̂) = Number of successes / Sample size = 1600 / 2000 = 0.8
Step 2: Calculate the standard error:
Standard Error (SE) = √[(p̂(1-p̂))/n]
where n is the sample size
SE = √[(0.8 * (1-0.8))/2000]
SE ≈ 0.0141
Step 3: Calculate the margin of error (ME)
ME = Z * SE
where Z is the critical value corresponding to the desired confidence level (0.95).
Using the Z-table or a calculator, we can find that the Z-value for a 0.95 confidence level is approximately 1.96.
ME = 1.96 * 0.0141 ≈ 0.0277
Step 4: Calculate the lower and upper bounds of the confidence interval:
Lower bound = Point estimate - ME
Upper bound = Point estimate + ME
Lower bound = 0.8 - 0.0277 ≈ 0.7723
Upper bound = 0.8 + 0.0277 ≈ 0.8277
Therefore, the interval estimate for the population proportion is approximately 77.2% to 82.8%, rounded to the nearest tenth of a percent.