Question

# 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.

DATA: 5.20, 5.72, 4.38, 4.80, 5.02, 5.16, 4.74, 5.19, 5.34, 4.76, 4.56, 4.68

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

A point estimate for the population mean is _______???? (round to 2 decimal places)

​(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 a 95​% probability that the true mean pH of rain water is between _____ and _______

B.There is a 95​% confidence that the population 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 99​% confidence that the population mean pH of rain water is between ____ and _____

B.There is a 99​%nprobability that the true mean pH of rain water is between ____ and ______

C.If repeated samples are​ taken, 99​% of them will have a sample pH of rain water 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

increases.

decreases.

This makes sense since

all confidence intervals of a given level of confidence have the same width.

including fewer numbers for consideration makes it more likely one of them is correct.

including more numbers for consideration makes it more likely one of them is correct.

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