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. 5.05 5.72 4.38 4.80 5.02 4.68 4.74 5.19 4.61 4.76 4.56 5.54 ​(a) Determine a point estimate for the population mean. A point estimate for the population mean is 4.92. ​(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 nothing and nothing. B. There is a 95​% probability that the true mean pH of rain water is between nothing and nothing. C. If repeated samples are​ taken, 95​% of them will have a sample pH of rain water 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. There is 99​% confidence that the population mean pH of rain water is between nothing and nothing. C. If repeated samples are​ taken, 99​% of them will have a sample pH of rain water 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 ▼ decreases. increases. This makes sense since ▼ including fewer numbers for consideration makes it more likely one of them is correct. 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.

Answer 1