Question

Suppose that the confidence interval (0.39,0.65) is given for a population proportion, p. Use these confidence interval limits to find the point estimate, p^​, and the margin of error, E. p^= E=

Answer 1

The point estimate, p^, for the population proportion given the confidence interval (0.39, 0.65) is 0.52, and the margin of error, E, is 0.13.

Step-by-step explanation:

The given confidence interval is (0.39, 0.65) for a population proportion, p. To find the point estimate, p^, and the margin of error, E, we need to calculate the middle of the interval for the point estimate and half the width of the interval for the margin of error.

The point estimate, p^, is the midpoint of the confidence interval and can be calculated by averaging the lower and upper bounds:

1. 
   
3. Add the lower and upper bounds of the confidence interval: 0.39 + 0.65 = 1.04.
4. 
   
6. Divide the sum by 2: 1.04 / 2 = 0.52.

So, the point estimate, p^, is 0.52.

To find the margin of error, E, subtract the point estimate from the upper bound of the confidence interval:

1. 
   
3. Subtract the point estimate from the upper bound: 0.65 - 0.52 = 0.13.

Therefore, the margin of error, E, is 0.13.

Answer 2

The point estimate is 0.52 and the margin of error is 0.13.

In a confidence interval for a population proportion p, the point estimate
`(\( \hat{p} \))` is the midpoint of the interval, and the margin of error E is half of the width of the interval.

The confidence interval is given as (0.39, 0.65). The point estimate and margin of error can be found as:

Point Estimate (
`\( \hat{p} \)`):

`\[ \hat{p} = \frac{\text{Lower Limit} + \text{Upper Limit}}{2} \]`

`\[ \hat{p} = (0.39 + 0.65)/(2) \]` = 0.52

Margin of Error (E):

E =
`\frac{\text{Upper Limit} - \text{Lower Limit}}{2}`

E =
`(0.65 - 0.39)/(2)` = 0.13

So, the point estimate (
`\( \hat{p} \)`) is found to be 0.52, and the margin of error (E) is calculated as 0.13.