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 + 5.585.58 5.72 4.624.62 4.80 5.02 4.684.68 4.74 5.19 5.345.34 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.

If repeated samples are​ taken,

9595​%

of them will have a sample pH of rain water between

nothing

and

nothing .

C.

There is a

9595​%

probability that the true mean pH of rain water is 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.

If repeated samples are​ taken,

9999​%

of them will have a sample pH of rain water between

nothing

and

nothing .

B.

There is a

9999​%

probability that the true mean pH of rain water is 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

▼

decreases.

increases.

This makes sense since

▼

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

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.

Answer 1

a. Point estimate of mean is

For standard deviation

Create the following table.

data	data-mean	(data - mean)2
5.58	0.5542	0.30713764
5.72	0.6942	0.48191364
4.62	-0.4058	0.16467364
4.8	-0.2258	0.05098564
5.02	-0.0058	3.364E-5
4.68	-0.3458	0.11957764
4.74	-0.2858	0.08168164
5.19	0.1642	0.02696164
5.34	0.3142	0.09872164
4.76	-0.2658	0.07064964
4.56	-0.4658	0.21696964
5.3	0.2742	0.07518564

b. t table value for n=12 for 95% CI is 2.201

So Margin of Error is

Hence CI is

A. There is 95​% confidence that the population mean pH of rain water is between 4.777 and 5.275

c. Now t table value for 99% CI is 3.106

So

Hence CI is

C. There is 99​% confidence that the population mean pH of rain water is between 4.674 and 5.378.

d. As the level of confidence​ increases, the width of the interval increases

This make sense since

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