Question

In: Statistics and Probability

The following data represent the pH of rain for a random sample of 12 rain dates....

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.

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

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

C. There is a 95​% probability that the true mean pH of rain water is 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 ______

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

Solutions

Expert Solution

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

A point estimate for the population mean is 5.04 ​(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. If repeated samples are​ taken, 95​% of them will have a sample pH of rain water between 4.8073 and 5.2727.

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.)

B. If repeated samples are​ taken, 99​% of them will have a sample pH of rain water between 4.7116 and 5.3684


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