Quiz 10 Hypothesis test using confidence interval • Name:

A road
x: cars/5 min
19
21
17
27
16

The data is the number of cars per five minute period passing past some place along some road somewhere on Pohnpei. Use the sample mean x and the sample standard deviation sx the data given in the table to calculate a 95% confidence interval for the population mean number of cars per five minute periods using the student's t-distribution.

  1. sample size: n = 5 (not the sum of the cars but the number of five minute samples!)
  2. x = ______________ Calculate the sample mean x number of cars per five minute period.
  3. sx = ______________ Calculate the sample standard deviation sx number of cars per five minute period.
  4. confidence level: c = ______________
  5. degrees of freedom: = ______________
  6. t-critical: tc = ______________
  7. Error tolerance E: = ______________
  8. Calculate the 95% confidence interval for the population mean number of cars per five minute period:

    P( ___________ ≤ ≤ ___________ ) = 0.95
  9. _________ The overall population mean for Pohnpei is 13.89 cars per five minute period. Is the population mean of 13.89 "inside" or "outside" the 95% confidence interval?
  10. _________ The overall population mean for Pohnpei is 13.89 cars per five minute period. Test the hypothesis that the road data in the table is statistically significantly different at a confidence level c of 95%. Is the road data given statistically significantly different from 13.89 at 95%?
  11. _________ Could the data above have come from a population with a mean of 13.89 at a 95% level of confidence?
  12. _________ Is the road statistically significantly busier (carrying more traffic on average) than the Pohnpei mean of 13.89 at a 95% level of confidence?
  13. Rerun your hypothesis test at a confidence level c of 0.99, that is, generate a 99% confidence interval.

    P( ___________ ≤ ≤ ___________ ) = 0.99
  14. _________ Could the data above have come from a population with a mean of 13.89 at a 99% level of confidence?
  15. _________ Is the road statistically significantly busier (carrying more traffic on average) than the Pohnpei mean of 13.89 at a 99% level of confidence?
Statistic or ParameterSymbolEquationsExcel
Confidence interval statistics
Degrees of freedom df = 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 an error tolerance E of a mean for any n ≥ 5 using sx. E error tolerance =tc*sx/SQRT(n)
Calculate a confidence interval for a population mean from the sample mean x and error tolerance E:   x-E ≤  ≤ x+E