MS 150 Statistics Fall 2006 Quiz 09 Chapter 9.1 ● Name:

1. _____ In statistics, can you construct a range (a confidence interval) from a sample mean, sample standard deviation, and sample size that will always include the population mean µ?
2. Why?
3. Last spring high school seniors took the College of Micronesian-FSM etnrance test. The mathematics portion of that test is used to place students at the appropriate level in mathematics. Nineteen of these new freshmen students were placed into a new developmental mathematics course called MS 096 Elementary Algebra.
        The division of mathematics wants to determine if the placement by the entrance test was appropriate for these students. While individual students pass or fail for their own individual reasons, the average of all of the students at midterm should be a good indicator of whether the students were placed correctly by the math entrance test. If the students were placed correctly, then their population mean µ score in the course should be a 70 or higher. If the population mean µ could be below 70 at midterm, then the students might not have been placed correctly, they might have been "overplaced."
        To determine the possible values of the population mean µ, construct a 95% confidence interval for the a sample size n = 19 students with a sample mean x = 76 with a sample standard deviation of sx = 12.
        Note that n < 30. Despite this, go ahead and use z and the normsinv function in your calculations. There were only 19 students placed into MS 096 Elementary Algebra. Next week we will learn how to adjust for an n less than 30. Note that when we calculate a positive z value for use in determining a confidence interval, we refer to that z as "z-critical" and use the abbreviation z_c.
   1. __________ What is x?
   2. __________ What is sx?
   3. __________ What is n?
   4. __________ What is c?
   5. __________ Use z_c = ABS(NORMSINV((1-c)/2)) to find the z-critical value.
   6. __________ Calculate the error E using $\text{E}=z_c\frac{sx}{\sqrt{n}}$
   7. Use x − E ≤ µ ≤ x + E to construct the 95% confidence interval for the population mean µ:
      
      ___________ ≤ µ ≤ ___________
   8. _____ Could the population mean µ be below 70?
   9. Run the same analysis as above using a 99% confidence interval. Write the calculated confidence interval below:
      ___________ ≤ µ ≤ ___________
   10. _____ Does the 99% confidence interval include the possibility of a population mean µ below 70?