Question

For a sample, the 95% confidence interval is (0.202, 0.482). What is the point estimate, \hat{p}, of this sample?

Answer 1

The point estimate, \(\hat{p}\), of a sample given a 95% confidence interval of (0.202, 0.482) is calculated by adding the lower limit to the upper limit and dividing by 2, resulting in a point estimate of 0.342.

Step-by-step explanation:

The point estimate, \(\hat{p}\), for a sample when given a 95% confidence interval like the one in your question, which is (0.202, 0.482), is the midpoint of the lower and upper bounds of this interval. You calculate it by adding the lower limit to the upper limit and then dividing by 2.

To find the point estimate:

1. Add the lower limit of the confidence interval to the upper limit: 0.202 + 0.482 = 0.684.
2. Divide this sum by 2 to get the midpoint: 0.684 / 2 = 0.342.

Therefore, the point estimate \(\hat{p}\) of the sample is 0.342.

Answer 2

The Point estimate p = 0.342

Step-by-step explanation:

For the sample, 95% confidence interval (0.202,0.482) . The Confidence interval width = (0.482 - 0.202) = 0.28

The margin of error = 0.28/2

The margin of error = 0.14

So, Point estimate p = Lower bound + Margin of error

Point estimate p = 0.202 + 0.14

Point estimate p = 0.342

Therefore, the Point estimate p = 0.342