Answer:
Explanation:
To construct a confidence interval for the standard deviation of the pH of rainwater in this region, we will use the following formula:
Lower bound: sqrt((n-1)s^2 / X^2)
Upper bound: sqrt((n-1)s^2 / Y^2)
where n is the sample size, s is the sample standard deviation, and X and Y are the values of the chi-squared distribution that correspond to the lower and upper bounds of the confidence interval, respectively.
First, we need to calculate the sample size and the sample standard deviation:
n = 12
s = 0.309
Next, we need to find the values of X and Y from the chi-squared distribution. Since we want a 90% confidence interval, and there are (n-1) = 11 degrees of freedom, we can find the values of X and Y that correspond to the 5th and 95th percentiles, respectively, using a chi-squared table or a calculator:
X = 3.816
Y = 20.483
Now we can substitute these values into the formula to find the lower and upper bounds of the confidence interval:
Lower bound: sqrt((n-1)s^2 / X^2) = sqrt((11)(0.309^2) / (3.816)^2) = 0.152
Upper bound: sqrt((n-1)s^2 / Y^2) = sqrt((11)(0.309^2) / (20.483)^2) = 0.554
Therefore, we can say with 90% confidence that the standard deviation of the pH of rainwater in this region is between 0.152 and 0.554.
Interpretation: We are 90% confident that the true standard deviation of the pH of rainwater in this region falls between 0.152 and 0.554. This means that if we were to take many random samples of rainwater from this region and calculate the standard deviation for each sample, about 90% of the resulting confidence intervals would contain the true standard deviation of the population.