The following data represent the pH of rain for a random sampleof 12 rain dates. A normal probability plot suggests the data couldcome from a population that is normally distributed. A boxplotindicates there are no outliers. Complete parts​ (a) through​ (d)below.

(a) Determine a point estimate for the population mean.

A point estimate for the population mean is ___. ​(Round to twodecimal places as​ needed.)

(b) Construct and interpret a 95​% confidence interval for themean pH of rainwater. Select the correct choice below and fill inthe answer boxes to complete your choice. ​(Use ascending order.Round to two decimal places as​ needed.)

A. If repeated samples are​ taken, 95​% of them will have asample pH of rain water between ___ and ___.

B. There is 95​% confidence that the population mean pH of rainwater is between ___ and ___.

C. There is a 95​% probability that the true mean pH of rainwater is between ___ and ___.

c) Construct and interpret a 99​% confidence interval for themean pH of rainwater. Select the correct choice below and fill inthe answer boxes to complete your choice. ​(Use ascending order.Round to two decimal places as​ needed.)

A. There is a 99​% probability that the true mean pH of rainwater is between ____ and ___.

B. If repeated samples are​ taken, 99​% of them will have asample pH of rain water between ____ and ___.

C. There is 99​% confidence that the population mean pH of rainwater is between ____ and ____.

(d) What happens to the interval as the level of confidence is​changed? Explain why this is a logical result. As the level ofconfidence​ increases, the width of the interval ____ This makessense since ______

HERE IS THE GIVEN DATA

5.05
5.72
4.99
4.80
5.02
4.68
4.74
5.19
5.43
4.76
4.56
5.54