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).
a)
A point estimate for the population mean is
b)
n=12
s = 0.4123
95% confidence interval
Formula
tc = 2.201 ( using ttable )
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 ttable )
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
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