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. 5.585.58 5.72 4.624.62 4.80 5.02 4.574.57 4.74 5.19 5.435.43 4.76 4.56 5.715.71 ​(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. There is a 9595​% probability that the true mean pH of rain water is between nothing and nothing. C. If repeated samples are​ taken, 9595​% of them will have a sample pH of rain water 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. There is 9999​% confidence that the population mean pH of rain water is between nothing and nothing. B. If repeated samples are​ taken, 9999​% of them will have a sample pH of rain water between nothing and nothing. C. There is a 9999​% probability that the true 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 the ▼ sample size margin of error point estimate ▼ increases as well. decreases as well.

Answer 1

a)

	pH of rain(x)
	5.58
	5.72
	4.62
	4.8
	5.02
	4.57
	4.74
	5.19
	5.43
	4.76
	4.56
	5.71
total	60.7

Here

n = 12

Therefore, the  point estimate for the population mean is 5.06 pH.

b)

	pH of rain(x)	x2
	5.58	31.1364
	5.72	32.7184
	4.62	21.3444
	4.8	23.04
	5.02	25.2004
	4.57	20.8849
	4.74	22.4676
	5.19	26.9361
	5.43	29.4849
	4.76	22.6576
	4.56	20.7936
	5.71	32.6041
total	60.7	309.2684

Here

n = 12

From the Z- table, the z-value for 95% confidence interval = 1.96

The 95% confidence interval for population mean is

  

( 4.81 , 5.31 )

The correct option is

A. There is 95​% confidence that the population mean pH of rain water is 4.81 pH and 5.31 pH.

C)

From the Z- table, the z-value for 99% confidence interval = 2.576

The 99% confidence interval for population mean is

  

( 4.73 , 5.39 )

The correct option is

A. There is 99% confidence that the population mean pH of rain water is 4.73 pH and 5.39 pH.

d)

As the level of confidence​ increases, the width of the interval increases. This makes sense since the margin of error increases as well.