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 5.58 5.72 5.24 5.24 4.80 5.02 5.03 5.03 4.74 5.19 4.87 4.87 4.76 4.56 4.91 4.91

​(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. If repeated samples are​ taken, 9595​% of them will have a sample pH of rain water between nothing and nothing. B. There is a 9595​% probability that the true mean pH of rain water is between nothing and nothing. C. There is 9595​% confidence that the population mean pH of rain water is between nothing and nothing

​(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​% probability that the true mean pH of rain water is between nothing and nothing. B. If repeated samples are​ taken, 99​% 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. all confidence intervals of a given level of confidence have the same width. including fewer numbers for consideration makes it more likely one of them is correct.

Answer 1

a. For given sample mean is calculated as

b. Now first we will find standard deviation

Create the following table.

data	data-mean	(data - mean)2
5.58	0.5182	0.26853124
5.58	0.5182	0.26853124
5.72	0.6582	0.43322724
5.24	0.1782	0.03175524
5.24	0.1782	0.03175524
4.80	-0.2618	0.06853924
5.02	-0.0418	0.00174724
5.03	-0.0318	0.00101124
5.03	-0.0318	0.00101124
4.74	-0.3218	0.10355524
5.19	0.1282	0.01643524
4.87	-0.1918	0.03678724
4.87	-0.1918	0.03678724
4.76	-0.3018	0.09108324
4.56	-0.5018	0.25180324
4.91	-0.1518	0.02304324
4.91	-0.1518	0.02304324

Now t table value for 16 df is 2.120

So Margin of Error is

Hence CI is

C. There is 95​% confidence that the population mean pH of rain water is between 4.89 and 5.23

c. For 99% CI, t table value is 2.921

So,

So CI is

C. There is 99​% confidence that the population mean pH of rain water is between 4.83 and 5.29

d. As the level of confidence​ increases, the width of the interval increases. This makes sense since including more numbers for consideration makes it more likely one of them is correct.