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.

 5.58 5.72 4.8 4.80 5.02 4.68 4.74 5.19 5.34 4.76 4.56 5.54

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

B. If repeated samples are​ taken, 95​% of them will have a sample pH of rain water between ______and _______.

C. There is 95​% confidence that the population 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. If repeated samples are​ taken, 99​% of them will have a sample pH of rain water between _________and _________.

B. There is 99​% confidence that the population mean pH of rain water is between ________and ________.

C. There is a 99​% probability that the true 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 ______________

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