Question

In a random sample of 800 adults in the United States, 450 say they used Zoom at least once during the last 10 days. We are asked to calculate a 95% confidence interval for the population parameter. What is the lower limit for this interval?

Answer 1

The lower limit of the 95% confidence interval for the proportion of American adults who have used Zoom at least once in the last 10 days is approximately 52.84%.

Step-by-step explanation:

To calculate the lower limit of a 95% confidence interval for the population parameter of American adults who have used Zoom at least once during the last 10 days, we can use the formula for a confidence interval of a population proportion:

CI = π ± Z*(√(π(1-π)/n))

Where π is the sample proportion, Z is the Z-value corresponding to the desired confidence level, and n is the sample size.

In this case, the sample proportion (π) is 450/800 = 0.5625. The Z-value for a 95% confidence interval is approximately 1.96 (found in Z-tables or with a calculator) and the sample size (n) is 800.

First, we calculate the standard error:
SE = √(π(1-π)/n) = √(0.5625*(1-0.5625)/800) ≈ √(0.2461/800) ≈ 0.0174

Now, calculate the margin of error:
Margin of Error (E) = Z*SE = 1.96*0.0174 = 0.034104

Finally, the lower limit of the confidence interval:
Lower Limit = π - E = 0.5625 - 0.034104 ≈ 0.5284

So, the lower limit of the 95% confidence interval for the proportion of American adults who have used Zoom at least once in the last 10 days is approximately 0.5284 or 52.84%.