MS 150 Statistics spring 2007 quiz 5 ● Name:

  1. _____ In statistics, can you construct a range (a confidence interval) from a sample mean, sample standard deviation sx, and sample size that will always include the population mean µ?
  2. Why?
  3. An experiment is conducted using a new way of sequencing radio packets on a wireless Internet link. A sample size n of 30 ping packets is sent with a slot duration of 32 milliseconds. The sample mean x round-trip-time of 50 milliseconds with a sample standard deviation sx of 19 milliseconds. The distribution of the round-trip-time is normal. Construct a 95% confidence interval for the mean round-trip-time. Use sx for σ.
    1. __________ What is x?
    2. __________ What is sx?
    3. __________ What is n?
    4. __________ What is the standard error of the mean?
    5. __________ What is c?
    6. __________ What is the area to the left of the lower limit?
    7. __________ Use the NORMINV function to find the lower limit of the 95% confidence interval for the mean.
    8. __________ What is the area to the left of the upper limit?
    9. __________ Use the NORMINV function to find the upper limit of the 95% confidence interval for the mean.
    10. __________ Write out the 95% confidence interval:
      ___________ ≤ µ ≤ ___________
    11. __________ Determine the margin of error E for the mean.
    12. Write out the 95% confidence interval in μ ± E format:
      __________ ± __________

Formulas are written for OpenOffice.org Calc. Replace semi-colons with commas for Excel.

Confidence interval statistics
Statistic or ParameterSymbolEquationsOpenOffice
Find the limit for a confidence interval for n ≥ 30 using a normal distribution with p as the area to the left of the limit =NORMINV(p;μ;σ/SQRT(n))
Degrees of freedomdf= n − 1=COUNT(data)-1
Find a tc value from a confidence level c and sample size n tc =TINV(1-c;n-1)
Calculate the margin of error E for a mean for any n ≥ 5 using sx. E error tolerance =tc*sx/SQRT(n)
Calculate a confidence interval for a population mean μ from the sample mean x and margin of error E for the mean. x − E ≤ μ ≤ x + E