Final answer:
To find the 92% confidence interval for the proportion of all adults in the US who are afraid of their identity being stolen, calculate the point estimate and margin of error. The point estimate is the proportion of the sample who indicated that they were afraid of their identity being stolen. The margin of error is calculated using the critical value and standard error. Finally, calculate the confidence interval by subtracting and adding the margin of error to the point estimate.
Step-by-step explanation:
To find the 92% confidence interval for the proportion of all adults in the US who are afraid of their identity being stolen, we first calculate the point estimate and the margin of error.
The point estimate is the proportion of the sample who indicated that they were afraid of their identity being stolen, which is 408/650 = 0.628.
Next, we calculate the margin of error using the formula: margin of error = critical value * standard error.
Since the confidence level is 92%, the critical value is 1.75 (found from a z-table).
The standard error is calculated as the square root of [(point estimate * (1 - point estimate)) / n], where n is the sample size.
Using the given values, the standard error is sqrt[(0.628 * (1 - 0.628)) / 650] = 0.015
Therefore, the margin of error is 1.75 * 0.015 = 0.026.
Finally, we can calculate the confidence interval by subtracting the margin of error from the point estimate and adding the margin of error to the point estimate.
The confidence interval is [0.628 - 0.026, 0.628 + 0.026] = [0.602, 0.654].
Therefore, the 92% confidence interval for the proportion of all adults in the US who are afraid of their identity being stolen is 60.2% to 65.4%.