Problem
The following data represent the $\mathrm{pH}$ of rain for a random sample of 12 rain dates. A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot indicates 5.30 5.72 4.38 4.80 5.02 4.57 4.74 5.19 4.61 4.76 4.56 5.68 there are no outliers. Complete parts a) through d) below. Click the icon to view the table of critical t-values. (a) Determine a point estimate for the population mean. A point estimate for the population mean is (Round to two decimal places as needed.)
Solution
Step 1 ：Given data is [5.3, 5.72, 4.38, 4.8, 5.02, 4.57, 4.74, 5.19, 4.61, 4.76, 4.56, 5.68].
Step 2 ：A point estimate for the population mean is calculated by summing up all the data points and dividing by the number of data points.
Step 3 ：The calculation is \(\frac{5.3 + 5.72 + 4.38 + 4.8 + 5.02 + 4.57 + 4.74 + 5.19 + 4.61 + 4.76 + 4.56 + 5.68}{12}\).
Step 4 ：After calculating, we get the mean as 4.944166666666667.
Step 5 ：Rounding to two decimal places, we get 4.94.
Step 6 ：So, the point estimate for the population mean is \(\boxed{4.94}\).
