For each question, calculate the confidence intervals as stated.

Question 1:The National Assessment of Educational Progress (NAEP) is administered annually to 4th, 8th, and 12th graders in the United States. On the math assessment, a score above 275 is considered an indication that a student has the skills to balance a checkbook. In a random sample of 500 young men between the ages of 18 and 20, the mean NAEP math score is 272 with a standard deviation of 35. Do we have evidence at the 95% confidence level to support the claim that young men nationwide have a mean score different than 275?

Answer:

Question 2:The National Center for Health Statistics reports that the systolic blood pressure for males 35 to 44 years of age has a mean of 128. In a study of business executives, a random sample of 101 executives has a mean systolic blood pressure of 134 and a standard deviation of 18.5. Do the data suggest that the mean systolic blood pressure for business executives is different than 128 with 95% confidence? What about with 90% confidence?

Question 3:The average age of residents in senior living communities is 84 in the United States. A health educator at Laurel Lake in Hudson, Ohio, has been using education materials geared toward that age but wants to know if the mean age at Laurel Lake differs significantly from the US average without surveying the entire population. She took a random sample of 21 residents and found the mean age to be 79 with a standard deviation of 10. Do the data suggest that the mean resident age at Laurel Lake is different from the US average?