Quiz 09 | 9 - 10 • Name:

The following problem is based on the garment (clothing) exports from the FSM. All numbers quoted are in 1000s of dollars in order to simplify the arithmetic. During a sample size n = 12 months of 2002 the sample mean was x = 308 (1000's of dollars) with a standard deviation of sx = 108. Calculate a 95% confidence interval for the expected range of the population mean based on the 12 month sample data using the student's t-distribution.

  1. sample size: n = ______________
  2. sample mean x = ______________
  3. sample standard deviation sx = ______________
  4. confidence level: c = ______________
  5. degrees of freedom: = ______________
  6. t-critical: tc = ______________
  7. Error tolerance E: = ______________
  8. Calculate the confidence interval for the population mean arrival time:

    P( ___________ ≤ ≤ ___________ ) = 0.95
  9. _________ The FSM has a population mean export value for garments of 248 (1000's of dollars) per month for six years between 1992 and 2002. Use 248 as the population mean . Does the 2002 sample mean monthly garment exports represent a statistically significant difference from the population mean at a 95% level of confidence?
  10. _________ Did the FSM generate a statistically significant higher mean monthly income in 2002 from garments at a 95% level of confidence?

Run another set of confidence interval calculations, this time calculating a 90% confidence level for the same monthly sample data.

  1. confidence level: c = ______________
  2. t-critical: tc = ______________
  3. Error tolerance E: = ______________
  4. Calculate the confidence interval for the population mean arrival time:

    P( ___________ ≤ ≤ ___________ ) = 0.90
  5. _________ The FSM has a population mean export value for garments of 248 (1000's of dollars) per month for six years between 1992 and 2002. Use 248 as the population mean . Does the 2002 sample mean monthly exports represent a statistically significant difference from the population mean at a 90% level of confidence?
  6. _________ Did the FSM generate a statistically significant higher mean monthly income in 2002 from garments at a 90% level of confidence?
  7. Tough and arguably tricky: Which analysis is correct and WHY?
Statistic or Parameter Symbol Equations Excel
Calculate a t-statistic t t xbartot.gif (1028 bytes) =(x - )/(sx/SQRT(n))
Find a tc value from a confidence level c and sample size n tc   =TINV(1-c,n-1)
Calculate an error tolerance E of a mean for any n ≥ 5 using sx. E error_tolerance_tc.gif (989 bytes) =tc*sx/SQRT(n)
Calculate a confidence interval for a population mean from a sample mean x and an error tolerance E   x-E≤ ≤x+E