Question

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.

Open in StatCrunch + Copy to Clipboard + Open in Excel + 5.205.20 5.72 4.384.38 4.80 5.02 4.684.68 4.74 5.19 5.435.43 4.76 4.56 5.305.30

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

A point estimate for the population mean is

nothing .

​(Round to two decimal places as​ needed.)

​(b) Construct and interpret a

9595​%

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

9595​%

confidence that the population mean pH of rain water is between

nothing

and

nothing .

B.

There is a

9595​%

probability that the true mean pH of rain water is between

nothing

and

nothing .

C.

If repeated samples are​ taken,

9595​%

of them will have a sample pH of rain water between

nothing

and

nothing .

​(c) Construct and interpret a

9999​%

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

9999​%

probability that the true mean pH of rain water is between

nothing

and

nothing .

B.

If repeated samples are​ taken,

9999​%

of them will have a sample pH of rain water between

nothing

and

nothing .

C.

There is

9999​%

confidence that the population mean pH of rain water is between

nothing

and

nothing .

​(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

▼

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

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

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

Answer 1

fro data n-l X0-39 a) Pofnt esttmotte s b) Popuatn mea PHbatn wat-en bett o een 4.43 and s.43 et los be 11ソ. c. .1-4.98士3.11 (0.39, 463, S 33 There fs 99ソ the populattor -Hat con Prdence 63 & S 32 consta evatron makes mote 1eKel