What critical value t* from Table C would you use for a confidence interval for the mean of the population in each of the following situations? (If you have access to software, you can use software to determine the critical values. Round your answers to three decimal places.) (a) A 95% confidence interval based on n = 18 observations.

Suppose you take a random sample of n = 80 Douglas College students and ask each student their age. You find that the mean age of students in this sample is X = 22.0375 years and the sample standard deviation is s = 3.2014 years.  Fill in the blanks (rounding to four decimal places):  The 95% confidence interval for the mean age μ of all Douglas College students is from ______ years to ______ years.

You are estimating how much population A's proportion of answering yes to a question exceeds population B's proportion who say yes to the same question by using a confidence interval. You have some ability to control the width of your interval. Which of the following would be most likely to ensure that the confidence interval is narrowed? O a. You increase both sample sizes and you decrease your confidence level. O b. You increase both sample sizes and you increase your confidence level. OC. You decrease both sample sizes and you increase your confidence level. O d. You decrease both sample sizes and you decrease your confidence level.

Suppose you are told that a 95% confidence interval for the average price of a gallon of regular gasoline in your state is from $3.37 to $3.60. Use the fact that the confidence interval for the mean is in the form x − E to x + E to compute the sample mean and the maximal margin of error E. (Round your answers to two decimal places.) x = $   E = $