Final answer:
To create a 95% confidence interval for the number of unhealthy days based on the AQI, calculate the mean, standard deviation, and use a t-distribution table to find the t-value, then compute the margin of error to add and subtract from the mean for the interval.
Step-by-step explanation:
The task is to construct a 95% confidence interval for the number of unhealthy days based on the AQI (Air Quality Index) for a given sample. To find the confidence interval, we first need to calculate the sample mean and the sample standard deviation. With the given data points, the mean (average) is calculated by summing all the values and dividing by the number of values, and the sample standard deviation is found by taking the square root of the variance, which is the average of the squared differences from the mean.
- Calculate the sample mean.
- Calculate the sample standard deviation.
- Find the degrees of freedom (df), which is one less than the sample size.
- Use a t-distribution table or software to find the appropriate t-value for a two-tailed 95 percent confidence interval with df degrees of freedom.
- Calculate the margin of error by multiplying the t-value by the standard deviation divided by the square root of the sample size.
- Add and subtract the margin of error from the sample mean to get the lower and upper bounds of the confidence interval.
Once you have these calculations, you can present the 95% confidence interval for the true mean number of unhealthy AQI days in metropolitan areas.