### Quiz 10 Hypothesis test using confidence interval • Name:

x: cars/5 min
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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 µ 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 µ number of cars per five minute period:

P( ___________ ≤ µ ≤ ___________ ) = 0.95
9. _________ The overall population mean µ for Pohnpei is 13.89 cars per five minute period. Is the population mean µ of 13.89 "inside" or "outside" the 95% confidence interval?
10. _________ The overall population mean µ 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( ___________ ≤ µ ≤ ___________ ) = 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 =tc*sx/SQRT(n)
Calculate a confidence interval for a population mean µ from the sample mean x and error tolerance E:   x-E ≤ µ ≤ x+E