Suppose we have a random sample of 300 people. 30 of these people are left handed. The upper limit of the 95% confidence interval for the proportion of people who are left handed is:
To calculate the upper limit of the 95% confidence interval for the proportion of people who are left-handed, we need to use the formula:
Upper limit = sample proportion + margin of error
The sample proportion is the number of left-handed people divided by the sample size: 30/300 = 0.1.
The margin of error is determined using the standard error formula:
Standard error = √((sample proportion * (1 - sample proportion)) / sample size)
Plugging in the values, we get:
Standard error = √((0.1 * 0.9) / 300) ≈ 0.01633.
Next, we need to find the critical value for a 95% confidence level. This can be looked up in a standard normal distribution table (z-table). For a two-tailed test, at a 95% confidence level, the critical value is approximately 1.96.
Finally, we can calculate the margin of error by multiplying the critical value with the standard error:
Margin of error = 1.96 * 0.01633 ≈ 0.032.
Now, we can calculate the upper limit of the 95% confidence interval:
Upper limit = 0.1 + 0.032 ≈ 0.132.
Therefore, the upper limit of the 95% confidence interval for the proportion of people who are left-handed is approximately 0.132.
To calculate the upper limit of the 95% confidence interval for the proportion of people who are left-handed, you can use the formula:
Upper limit = Sample proportion + (Z-score * Standard error)
Here's how to calculate it step-by-step:
Step 1: Calculate the sample proportion.
Sample proportion = Number of left-handed people / Total sample size
Sample proportion = 30 / 300
Sample proportion = 0.1
Step 2: Calculate the standard error.
Standard error = √((Sample proportion * (1 - Sample proportion)) / Sample size)
Standard error = √((0.1 * (1 - 0.1)) / 300)
Standard error ≈ 0.016
Step 3: Determine the Z-score for a 95% confidence level.
A 95% confidence level corresponds to a Z-score of approximately 1.96.
Step 4: Calculate the upper limit.
Upper limit = 0.1 + (1.96 * 0.016)
Upper limit ≈ 0.13
Therefore, the upper limit of the 95% confidence interval for the proportion of people who are left-handed is approximately 0.13.