Final answer:
To construct a 98% confidence interval for the number of unhealthy days based on the AQI for a random sample of metropolitan areas, calculate the mean and standard deviation of the sample. Then use the formula for margin of error to calculate the confidence interval.
Step-by-step explanation:
The question is asking you to construct a 98% confidence interval for the number of unhealthy days based on the Air Quality Index (AQI) for a random sample of metropolitan areas.
To construct the confidence interval, you will use the given data: (2.5, 5.5), (3.5, 6.5), (4.5, 7.5), and (5.5, 8.5).
Step 1: Calculate the mean of the sample, which is the average of the lower and upper bounds of each data interval.
Step 2: Calculate the standard deviation of the sample.
Step 3: Calculate the margin of error using the formula: margin of error = (critical value) * (standard deviation / square root of sample size).
Step 4: Calculate the confidence interval by subtracting the margin of error from the sample mean, and adding the margin of error to the sample mean.
The final confidence interval will give you an estimate for the true mean number of unhealthy days based on the AQI for all metropolitan areas.