Show work! ill) What is the margin of error for the interval calculated in part ii? (2 points)
1. Determine whether each of the following statements is true or false. (1.5 points each) i) TF The sample size required to obtain a confidence interval of specified margin of error m, increases as the confidence level increases. ii) T F The margin of error for a 95% confidence interval for the mean / decreases as the population standard deviation decreases. iii)T F The margin of error for a confidence interval for the mean /, based on a specified sample size n, increases as the confidence level decreases. iv)T F The margin of error for a 95% confidence interval for the mean / increases as the sample size increases. v) T F Take a SRS n=50 and calculate a 95% confidence interval. If we took a different sample of the same size, from the same population, and calculated a confidence interval with the same level of confidence, the margin of error would stay the same. vi)T F The higher the level of confidence for a confidence interval, the more precise the interval is. 2. Central Middle School has calculated a 95% confidence interval for the mean height () of 1 1-year old boys at their school and found it to be 56 + 2 inches or [54, 58]. Determine whether each of the following statements is true or false based on the information in the confidence interval. If you can't say that the statement is true based on the information provided by the confidence interval then it is false. (1/2 point each) i) T F There is a 95% probability that / is between 54 and 58. ii) T F There is a 95% probability that the true mean is 56, and there is a 95% chance that the true margin of error is 2. iii) T F If we took many additional random samples of the same size and from each computed a 95%confidence interval for /, approximately 95% of the time / would fall between 54 and 58. iv) T F If we took many additional random samples of the same size and from each computed a 95%confidence interval for /, approximately 95% of these intervals would contain /. v) T F 95% of 1 1-year old boys at Central Middle School are between 54 and 58 inches tall. vi) T F 95% of the sample of 1 1-year old boys at Central middle School were between 54 and 58 inches tall. 3. What would the z* value be for a 93% confidence level? (2 points) 4. In a simple random sample of 120 Kansas seniors you found the mean out-of-pocket health care expenses for 2008 to be $4, 897. Assume o=2, 125. i) How many people would you have to sample to estimate the mean out-of-pocket health care expenses in 2008 for all Kansas seniors to within $200 with 99% confidence? (5 points) ii) Calculate and interpret a 98% confidence interval for the mean out-of-pocket health care expenses in 2008 for all Kansas seniors. (5 points)
