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.

5.20 5.72 5.245 4.80 5.02 4.57 4.74 5.19 5.34 4.76 4.56 5.71

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Click the icon to view the table of critical​ t-values.

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

A point estimate for the population mean is BLANK

​(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 95​% confidence that the population mean pH of rain water is between BLANK AND BLANK

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

C. There is a 95​% probability that the true mean pH of rain water is between BLANK AND BLANK.

​(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 99​% confidence that the population mean pH of rain water is between BLANK AND BLANK.

B. If repeated samples are​ taken, 99​% of them will have a sample pH of rain water between BLANK AND BLANK.

C. There is a 99​% probability that the true mean pH of rain water is between BLANK and BLANK.

​(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

▼

sample size

margin of error

point estimate

▼

decreases as well.

increases as well.

Answer 1

a)

point estimate for the population mean=5.19

b)

for 95% CI; and 11 degree of freedom, value of t=					2.2010
margin of error E=t*std error                            =					0.253
lower confidence bound=sample mean-margin of error =					4.94
Upper confidence bound=sample mean+margin of error=					5.44

  95​% confidence interval for the mean =4.94 ; 5.44\

A. There is 95​% confidence that the population mean pH of rain water is between 4.94 AND 5.44

c)

for 99% CI; and 11 degree of freedom, value of t=					3.1060
margin of error E=t*std error                            =					0.357
lower confidence bound=sample mean-margin of error =					4.83
Upper confidence bound=sample mean+margin of error=					5.55

99​% confidence interval for the mean =4.83 ; 5.55

A.There is 99​% confidence that the population mean pH of rain water is between 4.83 AND 5.55

d)

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

This makes sense since the margin of error increases as well.