1. Answer the following confidence interval questions. (1) Carrie… 1. Answer the following confidence interval questions.(1) Carrie wants to construct 94% confidence interval for a population mean using normaldistribution.a. What is the alpha?b. Find the critical value for Z a/2 =(2) Damian wants to construct 90% confidence interval of a population mean. The populationstandard deviation, ? = 15, ? = 95, n = 25.a. What is the critical value Z a/2 ?b. What is the margin of error, E (rounded to 3 decimal places)?c. Construct a 90% confidence interval to estimate the population mean (rounded to 3decimal places)2. Sarah wants to construct 99% confidence interval of a population mean weight of the 2ndgraders at an elementary school. A sample of 32 randomly selected students at this schoolshows that the mean weight is 53 pounds with the standard deviation, 6 pounds.(1) What distribution do we use: Standard normal distribution or t-distribution ?(2) Find the critical value (rounded to 3 decimal places):(3) Find the margin of error, E (rounded to 3 decimal places).:(4) Construct a 99% confidence interval to estimate the population mean (rounded to 3decimal places).3. A company that produces detergents wants to estimate the mean amount of detergent in 64-ounce jugs at a 97% confidence level. The company knows that the standard deviation of theamounts of detergent in all such jugs is ? = .20 ounce. How large a sample should thecompany select so that the estimate is within a margin of error of .05 ounce?4. Download the data, ChildOutlook.xlsx from Blackboard.(1) Find ? , the sample proportion of the adults who answered ‘No’ to the question whetherthey believed that today’s children would be better off than their parents.(2) Find the critical value, Z a/2 for 90% confidence level (rounded to 3 decimal places.)(3) Find the margin of error, E (rounded to 3 decimal places.):(4) Construct a 90% confidence interval for the population proportion of adults who believethat today’s children will be better off than their parents.5. Refer to question number 4. Suppose that you want a .90 probability that the sampleproportion is within .02 of the population proportion of the adults who answered ‘No’ tothe question whether they believed that today’s children would be better off than their parents.(1) How large a sample size is needed to meet the required precision? Assume that ? isobtained from a previous sample. A known sample proportion is the same value as inquestion number 4.(2) How large a sample size is needed to meet the required precision?Assume that ? is not available.MathStatistics and Probability STA MISC
