Step 1 :Given the data set of pH values of rainwater, we are asked to find the point estimate for the population mean and a 95% confidence interval for the mean pH of rainwater.
Step 2 :The point estimate for the population mean is simply the sample mean, which can be calculated by summing all the values and dividing by the number of values.
Step 3 :The 95% confidence interval for the mean pH of rainwater can be calculated using the formula for a confidence interval: \(\bar{x} \pm t_{\alpha/2} \cdot \frac{s}{\sqrt{n}}\), where \(\bar{x}\) is the sample mean, \(t_{\alpha/2}\) is the t-value for a 95% confidence interval, \(s\) is the sample standard deviation, and \(n\) is the sample size.
Step 4 :Using the given data, we calculate the sample mean to be approximately 4.96.
Step 5 :We also calculate the sample standard deviation to be approximately 0.46.
Step 6 :The sample size is 11.
Step 7 :Using a t-distribution table, we find that the t-value for a 95% confidence interval with 10 degrees of freedom (n-1) is approximately 2.23.
Step 8 :Substituting these values into the confidence interval formula, we find the 95% confidence interval for the mean pH of rainwater to be approximately between 4.65 and 5.27.
Step 9 :Final Answer: The point estimate for the population mean is \(\boxed{4.96}\). There is 95% confidence that the population mean pH of rain water is between \(\boxed{4.65}\) and \(\boxed{5.27}\).