The following data represent the 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 there are no outliers. Complete parts a) through d) below.

data table

5.30 5.72 4.99 4.80 5.02 4.58 4.74 5.19 5.34 4.76 4.56 5.71

a) Determine a point estimate for the population mean.

A point estimate for the population mean is _.

(Round to two decimal places as needed.)

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

A.There is 95 % confidence that the population mean pH of rain water is between __and___.

B.There is a 95 % probability that the true mean pH of rain water is between__and__.

C.If repeated samples are taken, 95 % of them will have a sample pH of rain water between __and___.

(c) Construct and interpret a 99 % confidence interval for the mean pH of rainwater. Select the correct choice below and fill in the 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 rain water is between __and__.

B.If repeated samples are taken, 99 % of them will have a sample pH of rain water between __

and__.

C.There is 99 % confidence that the population mean pH of rain water 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 of confidence increases, the width of the interval _____. This makes sense since the ___ ____

decreases as well.

increases as well.