Quiz 11: Part IV Hypothesis testing • Name:

Gnihton
stegdiw length
/retems
4.7
4.8
4.9
5.0
5.1

On the planet Tau Centauri IV-2 the Gnihton corporation produces stegdiws. A stegdiw should be 5 retems long. Allegations arose from customers that Ghihton was producing stegdiws that were too short. An inspector from the Coordinating Council for Clarity in Commerce and Competition (C5) collected a random sample n of five stegdiws. The measure of each of the five stegdiws collected is given in the table. Run a hypothesis test to determine whether the five stegdiws could or could not have come from a population of stegdiws with a population mean length of 5 retems at a 5% level of significance. Use a population mean of 5 retems.

  1. _________ What level of measurement is the data?
  2. _________ Determine the sample size n.
  3. _________ Calculate the sample mean x.
  4. _________ Determine the median.
  5. _________ Determine the mode.
  6. _________ Determine the minimum.
  7. _________ Determine the maximum.
  8. _________ Calculate the range.
  9. _________ Calculate the sample standard deviation sx.
  10. _________ Calculate the sample Coefficient of Variation.
  11. ________________________________________ Write the null hypothesis in formal statistical format.
  12. ________________________________________ Write the alternate hypothesis in formal statistical format.
    α = 0.05.
  13. tc = __________ Determine tcritical.
  14. t = __________ Calculate the t-statistic.
  15. p = __________ Determine the p-value using the t-distribution.
  16. __________ What is the largest confidence interval c for which this difference is statistically significant?
  17. ________________________________________ Would we reject the null hypothesis or fail to reject the null hypothesis that the sample mean is statistically significantly different from the population mean at a 5% level of significance?
  18. __________ If we reject the null hypothesis, what is the risk of a type I error based on the p-value?
  19. __________ Can the C5 prove that the Gnihton corporation is producing stegdiws that are too short at a 5% level of confidence?
Hypothesis Testing
Calculate t-critical for a two-tailed test tc=TINV(α;df)
Calculate a t-statistic t xbartot.gif (1028 bytes) =(x - )/(sx/SQRT(n))
Calculate a two-tailed p-value from a t-statisticp = TDIST(ABS(t);df;2)