Question

III Question Help U The following data represent the pH of rain for a random sample of 12 rain dates. A normal probability plot suxests 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 5.02 5 34 5.72 4.58 4.76 5.24 4.74 4.56 4.80 5.19 5.70 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 I. (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) O A. There is a 95% probability that the true mean pH of rain water is between and OB. There is 95% confidence that the population mean pH of rain water is between OC. If repeated samples are taken, 95% of them will have a sample pH of rain water between and and Click to select your answer(s) is course at Summer 200 based on Sulivan Statistics informed usions Using Data,

Answer 1

Here, we have Sample size(n) = 12 60.7 Sample mean (X) = xi/n =5.0583 12 Standard deviation (s) = -120 -2(x - x)2 (n-1) 1 = (5.05 – 5.0583)2 + ........ +(5.70 – 5.0583)^2) (12-1) =0.3948 a)Point Estimate of the population mean (X)=5.06 (b)At 95% confidence interval a a=1-0.95 =0.05 =0.025 2 degree of freedom (df)=n-1=12-1 =11 tcritical=t0.025,11 = 2.201

95% confidence interval for mean (u) =X + tcritical 0.3948 = 5.06 + 2.201 * V12 = 5.06 + 0.2508 = 4.8092,5.3108 = 4.81, 5.31 (Round to two decimal places) b)There is 95% confident that the population mean PH of rain water is between 4.81 and 5.31. c) At 99% confidence interval a a=1-0.99 =0.01 =0.005 2 degree of freedom (df)=n-1=12-1 =11 tcritical to.005,11 = 3.106

99% confidence interval for mean (u) = = + tcritical = 5.06 + 3.106 *0.3948 V12 = 5.06 + 0.3540 = 4.706,5.414 = 4.71,5.41 (Round to two decimal places) There is 99% confidence that mean PH of rainwater is between 4.71 and 5.41. d)As the level of confidence interval increase , the width of interval increase. This makes sense since the critical value increases.