In: Statistics and Probability
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.
(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. If repeated samples are taken, 95% of them will have a sample pH of rain water between ___ and ___.
B. There is 95% confidence that the population mean pH of rain water is between ___ and ___.
C. There is a 95% probability that the true mean pH of rain water is 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% probability 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 ____ This makes sense since ______
HERE IS THE GIVEN DATA
5.05
5.72
4.99
4.80
5.02
4.68
4.74
5.19
5.43
4.76
4.56
5.54
(a) Determine a point estimate for the population mean.
A point estimate for the population mean is 5.04 (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. If repeated samples are taken, 95% of them will have a sample pH of rain water between 4.8073 and 5.2727.
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.)
B. If repeated samples are taken, 99% of them will have a sample pH of rain water between 4.7116 and 5.3684