Question

Suppose 250 randomly selected people are surveyed to determine if they own a tablet. Of the 250 surveyed, 98 reported owning a tablet. Using a 95% confidence level, compute a confidence interval. Please provide the necessary code and calculations in R.

Answer 1

To compute a confidence interval for the proportion of people who own tablets in this survey, use the formula CI = p ± z * sqrt((p * (1-p)) / n), where p is the sample proportion, z is the Z-score for the desired confidence level, and n is the sample size.

Step-by-step explanation:

To compute a confidence interval for the proportion of people who own tablets, we can use the formula:

CI = p ± z * sqrt((p * (1-p)) / n)

Where:
CI = Confidence Interval
p = Sample proportion
z = Z-score for the desired confidence level
n = Sample size

Plugging in the values from the given information:
p = 98/250 = 0.392
n = 250
Using a 95% confidence level, the z-score is 1.96

Substituting the values into the formula:
CI = 0.392 ± 1.96 * sqrt((0.392 * (1-0.392)) / 250)

Simplifying the equation:
CI = 0.392 ± 1.96 * sqrt((0.243536) / 250)

Calculating the square root and the final confidence interval:
CI = 0.392 ± 1.96 * 0.030984
CI ≈ (0.330, 0.454)