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.

5.58	5.72	4.38	4.80
5.02	5.03	4.74	5.19
4.61	4.76	4.56	5.30

​(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% chance that the true mean pH of rain water is between ___ and ___

B.There is 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 a 99​% chance 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 ___(decreases / increases).

This makes sense since the ___ (margin of error / sample size/ point estimate) ____(increases as well / decreases as well).

Answer 1

a)

A point estimate for the population mean is

b)

n=12

s = 0.4123

95% confidence interval

Formula

tc = 2.201 ( using t-table )

95 % confidence interval is

option B is correct

B.There is 95​% confidence that the population mean pH of rain water is between 4.712 and 5.236

c)

99% confidence interval

Formula

tc =3.106 ( using t-table )

99% confidence interval is

option C is correct

C.There is 99​% confidence that the population mean pH of rain water is between 4.6045 and 5.3439

​(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

This makes sense since the margin of error increases as well