Question

An environmental agency is examining the relationship Dependent variable is: Ozone between the ozone level (in parts per million) and the R squared =75.9% population (in millions) of a number of cities. Part of the regression analysis is shown to the right. Complete parts a and b. a) Give a 90% confidence interval for the approximate increase in ozone level associated with each additional million city inhabitants. Each additional million residents corresponds to an increase in average ozone level of between and ppm, with 90% confidence. (Round to two decimal places as needed. Use ascending order.) b) For the cities studied, the mean population was 1.7 million people. The population of a particular city is approximately 0.9 million people. Predict the mean ozone level for cities of that size with an interval in which you have 90% confidence. The mean ozone level for cities with 0.9 million people is between and ppm, with 90% confidence. (Round to two decimal places as needed. Use ascending order.)

Answer 1

To create a 90% confidence interval for the approximate increase in ozone level associated with each additional million city inhabitants, use the R squared value and regression analysis. To predict the mean ozone level for cities with a population of 0.9 million people, use the regression equation and calculate the margin of error.

Step-by-step explanation:

To create a 90% confidence interval for the approximate increase in ozone level associated with each additional million city inhabitants, you can use the R squared value of 75.9%. The formula for the confidence interval is: (R squared * population standard deviation) +/- (critical value * standard error of the slope). The critical value can be found using the t-distribution table for the desired confidence level and the degrees of freedom. The standard error of the slope can be calculated as: SE = (standard deviation of ozone level) / sqrt(sum of squares of (x - mean of x)). Once you have all the values, you can plug them into the formula to find the confidence interval.

To predict the mean ozone level for cities with a population of 0.9 million people, you can use the regression equation obtained from the analysis. The formula for predicting the mean ozone level is: predicted ozone level = intercept + (slope * population). Plug in the given values and calculate the predicted ozone level. Then, calculate the margin of error using the formula: margin of error = (critical value * standard deviation of residuals) / sqrt(sample size). Finally, create the confidence interval by adding and subtracting the margin of error from the predicted ozone level.

Answer 2

To calculate the confidence interval for the increase in ozone level associated with each additional million city inhabitants, we need to use the coefficient of the population variable from the regression analysis. To predict the mean ozone level for cities with a population of 0.9 million people, we need to use the coefficient of the population variable again.

Step-by-step explanation:

a) To calculate the confidence interval for the increase in ozone level associated with each additional million city inhabitants, we need to use the coefficient of the population variable from the regression analysis.

Assuming the coefficient is positive, we can calculate the standard error of the coefficient by taking the square root of the mean squared error (MSE) divided by the sum of the squares of the population variable values. Then, we can use the t-distribution to find the t-value that corresponds to a 90% confidence level for the given degrees of freedom.

Finally, we multiply the standard error by the t-value and add/subtract the result from the coefficient to get the lower/upper bounds of the confidence interval.

b) To predict the mean ozone level for cities with a population of 0.9 million people, we need to use the coefficient of the population variable again.

Multiply the coefficient by the population value, and then add/subtract the standard error of the coefficient multiplied by the t-value corresponding to a 90% confidence level. The resulting range will give us the confidence interval for the mean ozone level.