### Quiz 08 | 9 & 10 • Name:

During the period 1971 to 2002 there was a sample size n = 31 named tropical storms and typhoons with a sample mean was x = 18.4 with a standard deviation of sx = 3.4. Calculate a 95% confidence interval for the expected range of the population mean µ based on the 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( ___________ ≤ µ ≤ ___________ ) = 0.95
9. _________ If the mean number of storms since that period were 21 per season, would that be statistically significantly different at a 95% level of confidence? Use 21 as the population mean µ.

Use a population mean µ = 21 for the following hypothesis test. Use an alpha α = 0.05. For the sample size, sample mean, and sample standard deviation, refer to the introductory paragraph.
10. Write out the null hypothesis:
11. Write out the alternate hypothesis:
12. _________ What is alpha α?
13. _________ How many degrees of freedom are there?
14. _________ Determine tc
15. _________ Find the t-statistic t.
16. Do we:
1. ___ Reject the null hypotheis? OR
2. ___ Fail to reject the null hypothesis?

17. ___________________________ Is the sample mean number statistically significantly different from the population mean number of storms?
18. _________ What is the p-value for this hypothesis test?
19. _________ What is the largest possible confidence interval, max c, for which this difference is significant?
Statistic or Parameter Symbol Equations Excel
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 a sample mean x and an error tolerance E   x-E≤ µ ≤x+E
Statistic or Parameter Symbol Equations Excel
Hypothesis Testing
Degrees of freedom df = n-1 =COUNT(data)-1
Calculate a t-statistic (t) t (x - µ)/(sx/sqrt(n))
Calculate t-critical for a two-tailed test tc =TINV(α,df)
Calculate a p-value from a t-statistic t p = TDIST(ABS(t),df,#tails)
Calculate a maximum possible level of confidence c from a p-value (two-tailed) max c = 1-p