Question

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:

Answer 1

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.