Question

Construct a 95% confidence interval of the population proportion using the given information x=60, n=300 Click here to view the table of critical values. tents The lower bound is The upper bound is (Round to three decimal places as needed.) ccess Library ptions Enter your answer in the edit fields and then click Check Answer Clear A All parts showing

Answer 1

To construct a 95% confidence interval for the population proportion, we can use the formula: Lower Bound = sample proportion - margin of error, Upper Bound = sample proportion + margin of error. Using x = 60 and n = 300, the sample proportion is 0.2. The critical value associated with a 95% confidence level is approximately 1.96. Using the standard error formula, we find the standard error to be approximately 0.0237. The margin of error is then calculated to be approximately 0.0466. Therefore, the 95% confidence interval for the population proportion is approximately (0.1534, 0.2466).

Step-by-step explanation:

To construct a confidence interval for a population proportion, we can use the formula:

Lower Bound = sample proportion - margin of error

Upper Bound = sample proportion + margin of error

Given that we have x = 60 successes out of n = 300 trials, the sample proportion is x/n = 60/300 = 0.2.

The margin of error can be calculated as:

Margin of Error = critical value * standard error

Since we have a 95% confidence interval, we need to find the critical value associated with a 95% confidence level.

Using the table of critical values, we find that the critical value is approximately 1.96.

The standard error is given by: √[(sample proportion * (1 - sample proportion)) / n]

Plugging in the values, the standard error is √[(0.2 * (1 - 0.2)) / 300] = √(0.00056) ≈ 0.0237.

Now, we can calculate the margin of error: Margin of Error = 1.96 * 0.0237 ≈ 0.0466.

Finally, we can construct the confidence interval using the formula:

Lower Bound = 0.2 - 0.0466 ≈ 0.1534

Upper Bound = 0.2 + 0.0466 ≈ 0.2466

Therefore, the 95% confidence interval for the population proportion is approximately (0.1534, 0.2466).