sb1 q09 10.3 • Name:

18 November 2011

The data is a sample of the times of arrival for the first byte for a web page request sent via a home ADSL connection. At work the average arrival time for the first byte is 1160 milliseconds. Calculate the sample size, sample mean, and sample standard deviation for the sample data. You will find that the mean is less than 1160 ms. Lower times generally mean faster web page load. Below you will run a confidence interval and hypothesis test to explore whether the home ADSL line is statistically significantly faster than the college internet connection.

1. n = __________ Calculate the sample size n.
2. x = __________ Calculate the sample mean x.
3. sx = __________ Calculate the sample standard deviation sx.
4. SE = __________ Calculate the standard error SE.
5. t_c = ____________________ Given a confidence level c = 0.95, calculate the value of t_critical
6. E = _________ Calculate the margin of error E for the sample mean x.
7. Write out the 95% confidence interval for the range of the possible population mean μ
   p(_____________ < μ < ___________) = 0.95
8. _______________ Is 1160 ms a possible population mean for the sample data?
9. _______________ Is the home ADSL line statistically significantly faster than the college connection at a confidence level of 95%?
10. Write out the null hypothesis that the population mean μ is 1160 ms:
    H₀:
11. Write out the alternate hypothesis that the pop. mean μ is NOT 1160 ms:
    H₁:
    
    Run a hypothesis test at a risk of a type I error alpha α = 0.05
12. t = ____________________ Calculate the value of the t-statistic t
13. p-value = ____________________ Use =tdist(abs(t),n−1,2) to calculate the p-value.
14. ____________________ Calculate the maximum confidence we can have that the sample mean does not come from a population with a mean value of 1160 by calculating 1 − p-value.
15. ____________________ Is the sample mean x statistically significantly different from the population mean μ of 1160 ms?
16. _____________________ At an alpha α of 5%, would you fail to reject |or| reject the null hypothesis?
17. _______________ Is the home ADSL line statistically significantly faster than the college connection at an alpha (risk of a type one error) of 5%?